Chapters
Chiarella, C., Kang, B., Meyer, G. & Ziogas, A. 2014, 'Computational methods for derivatives with early exercise features' in Schmedders, K. & Judd, K.L. (eds), Handbook of Computational Economics, Elsevier, Netherlands, pp. 225-275.
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Chiarella, C. 2014, 'What's Beyond? Some Perspectives on the Future of Mathematical Finance' in Dieci, R., He, X. & Hommes, C. (eds), Nonlinear Economic Dynamics and Financial Modelling: Essays in Honour of Carl Chiarella, Springer, pp. 19-29.
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Bohm, V., Chiarella, C., He, X. & Huls, T. 2013, 'A homoclinic route to volatility: Dynamics of asset prices under autoregressive forecasting' in Bischi, G.I., Chiarella, C. & Sushko, I. (eds), Global analysis of dynamic models in economics and finance: Essays in honour of Laura Gardini, Springer, Germany, pp. 289-316.
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The article investigates the impact of mean-reverting forecasts in a model of asset pricing with two groups of investors under market clearing. Fundamentalists believe that asset prices follow an exogenous stochastic process, while chartists assume that asset prices follow a stochastic geometric decay process. For high values of mean reversion a period-doubling bifurcation occurs followed by a Neimark-Sacker bifurcation, after which homoclinic points exist inducing chaotic dynamics. Before the occurrence of homoclinic points, all orbits induce significant fluctuations with recurring symmetries and nonvanishing autocorrelations in all time series of prices and returns. After the homoclinic bifurcation, prices and returns follow alternating phases with low fluctuations near the steady state followed by phases with large excursions from the steady state. This shows that nonlinearities of the deterministic model rather than random perturbations are the causes of volatility clustering and of the generation of fat tails. Autocorrelations of prices and returns vanish while those of absolute returns and squared returns persist for high-order lags. Thus, the model is able to reproduce some important empirical market features
Chiarella, C., Huang, N. & Chi-Fai Lo, E. 2013, 'Credit portfolio correlations with dynamic leverage ratios' in Rösch, D. & Scheule, H. (eds), Credit Securitisations and Derivatives: Challenges for the Global Markets, Wiley, Australia, pp. 71-94.
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This chapter extends the dynamic leverage ratio model of of Hui et al. to the two-firm case so as to study the implications for default correlations and joint survival probabilities. The two-firm model has been proposed by Zhou, who extends the one-firm model of Black and Cox to the two-firm situation. The chapter reviews the techniques used by the authors to solve the first-passage-time problem: the method of images and the time varying barrier technique for dealing with time-dependent parameters. The chapter presents the numerical results for the impact on joint survival probabilities and default correlations across a range of different scenarios, for example, different correlation levels, drift rates, volatilities and initial leverage ratios
Chiarella, C. & Di Guilmi, C. 2013, 'A reconsideration of the formal Minskyan analysis: Microfoundations, endogenous money and the public sector' in Bischi, G.I., Chiarella, C. & Sushko, I. (eds), Global analysis of dynamic models in economics and finance: Essays in honour of Laura Gardini, Springer, Germany, pp. 63-81.
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The paper presents a survey of the literature that has grown out of the work of Hyman Minsky and, in particular, of the main models which have mathematically formalised the cyclical dynamics of a capitalist economy implied by the Financial Instability Hypothesis. We identify some of the issues that the existing literature has left unsolved. We then briefly summarise the contributions by Chiarella and Di Guilmi (J Econ Dyn Control 35(8):11511171, 2011c) and (Stud Nonl Dyn Econom forthcoming, 2012), highlighting how these papers have addressed the open questions and how they could be further developed.
Chiarella, C., Flaschel, P. & Semmler, W. 2013, 'Keynes, the dynamic stochastic general equilibrium model, and the business cycle' in Ryuzo Kuroki (ed), Keynes and Modern Economics, Routledge, New York, USA, pp. 85-116.
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Keynes in his General Theory has extensively responded to and criticized the classical economics that was dominant at his time. This paper elaborates on how Keynes would have responded to the dynamic stochastic general equilibrium (DSGE) model, or its more popular version, the real business cycle model, that appears to dominate macroeconomics today. Recently also many New Keynesians have employed this new paradigm in macroeconomics. We will discuss some major macroeconomic issues and show how differences in traditional Keynesian and the DSGE models may arise.4 We will also pursue a further more detailed study of why certain Keynesian ideas can usefully be applied to modem macroeconomics. This will help to resolve some important puzzles of modem macroeconomic theory.
Cheang, G.H. & Chiarella, C. 2012, 'A modern view on Merton's jump-diffusion model' in Cohen, S.N., Madan, D., Siu, T.K. & Yang, H. (eds), Advances in Statistics, Probability and Actuarial Science: Stochastic Processes, Finance and Control, World Scientific, USA, pp. 217-234.
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Chiarella, C., Flaschel, P. & Semmler, W. 2012, 'A macrodynamic model of real-financial interaction: Implications of budget equations and capital accumulation' in Progress in Financial Markets Research, Nova Science Publishers, Inc., pp. 243-262.
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Chiarella, C., Dieci, R. & He, X.-.Z. 2010, 'A framework for CAPM with heterogeneous beliefs' in Nonlinear Dynamics in Economics, Finance and Social Sciences: Essays in Honour of John Barkley Rosser Jr, Springer Berlin Heidelberg, pp. 353-369.
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The Sharpe-Lintner-Mossin (Sharpe 1964; Lintner 1965; Mossin 1966) Capital Asset Pricing Model (CAPM) plays a central role in modern finance theory. It is founded on the paradigm of homogeneous beliefs and a rational representative agent. However, froma theoretical perspective this paradigmhas been criticized on a number of grounds, in particular concerning its extreme assumptions about homogeneous beliefs, information about the economic environment, and the computational ability on the part of the rational representative economic agent. The impact of heterogeneous beliefs among investors on the market equilibrium price has been an important focus in the CAPM literature. A number of models with investorswho have heterogeneous beliefs have been previously studied. 1 A common finding in this strand of research is that heterogeneous beliefs can affect aggregate market returns. However, the question remains as to how exactly does heterogeneity affect themarket risk of risky assets? In much of this earlier work, the heterogeneous beliefs reflect either differences of opinion among the investors2 or differences in information upon which investors are trying to learn by using some Bayesian updating rule.3 Heterogeneity has been investigated in the context of either CAPM-like mean-variancemodels (for instance, Lintner 1969; Miller 1977;Williams 1977; and Mayshar 1982) or Arrow-Debreu contingent claims models (as in Varian 1985;Abel 1989; 2002; and Calvet et al. 2004). © 2010 Springer-Verlag Berlin Heidelberg.
Chiarella, C., Ziogas, A. & Ziveyi, J. 2010, 'Representation of American Option Prices Under Heston Stochastic Volatility Dynamics Using Integral Transforms', pp. 281-315.
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Chiarella, C., Dieci, R. & He, X. 2009, 'Heterogeneity, market mechanisms and asset price dynamics' in Hens, T. & Schenk-Hoppe, K.R. (eds), Handbook of Financial Markets: Dynamics and Evolution, Elsevier, USA, pp. 277-344.
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Chiarella, C., Meyer, G. & Ziogas, A. 2008, 'Pricing American Options Under Stochastic Volatility and Jump-Diffusion Dynamics' in Muller, K. & Steffens, U. (eds), Die Zukunft der Finanzdienstleistungs-industrie in Deutschland, Frankfurt School Verlag, Frankfurt, Germany, pp. 213-236.
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Chiarella, C., El-Hassan, N. & Kucera, A. 2008, 'The evaluation of discrete barrier options in a path integral framework' in Kontoghiorghes, E., Rustem, B. & Winker, P. (eds), Computational Methods in Financial Engineering: Essays in Honour of Manfred Gilli, Springer, Germany, pp. 117-144.
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The pricing of discretely monitored barrier options is a difficult problem. In general, there is no known closed form solution for pricing such options. A path integral approach to the evaluation of barrier options is developed. This leads to a backward recursion functional equation linking the pricing functions at successive barrier points. This functional equation is solved by expanding the pricing functions in Fourier-Hermite series. The backward recursion functional equation then becomes the backward recurrence relation for the coefficients in the Fourier-Hermite expansion of the pricing functions. A very efficient and accurate method for generating the pricing function at any barrier point is thus obtained. A number of numerical experiments with the method are performed in order to gain some understanding of the nature of convergence. Results for various volatility values and different numbers of basis functions in the Fourier-Hermite expansion are presented. Comparisons are given between pricing of discrete barrier option in the path integral framework and by use of finite difference methods.
Chiarella, C. & He, X. 2008, 'An adaptive model of asset price and wealth dynamics in a market with heterogeneous trading strategies' in Seese, D., Weinhardt, C. & Schlottmann, F. (eds), Handbook on Information Technology in Finance, Springer, Germany, pp. 465-499.
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The traditional asset-pricing models such as the capital asset pricing model (CAPM) of [42] and [34], the arbitrage pricing theory (APT) of [40], or the intertemporal capital asset pricing model (ICAPM) of [38] have as one of their important assumptions, investor homogeneity. In particular the paradigm of the representative agent assumes that all agents are homogeneous with regard to their preferences, their expectations and their investment strategies.1 However, as already argued by Keynes in the 1930s, agents do not have sufficient knowledge of the structure of the economy to form correct mathematical expectations that would be held by all agents
Asada, T., Chiarella, C., Flaschel, P. & Franke, R. 2007, 'Interacting Two-Country Business Fluctuations: Euroland and the USA' in Mazzi, G. & Savio, G. (eds), Growth and Cycle in the Eurozone, Palgrave Macmillan, New York, USA, pp. 109-118.
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This book presents recent theoretical and empirical advances on business cycles analysis with particular attention to Euro-zone characteristics. It also identifies applications of sophisticated tools by private and public institutions involved in the analysis of economic fluctuations and seeks to increase interaction between the academics, researchers and institutions in the area of business cycle analysis. This volume encompasses methodological advances in several important areas for business cycle analysis, such as multivariate statistical methods, synchronization and convergence, composite indicators, turning points dating and detection, output gap measurement, as well as innovative applications of the existing theories and methods to the economy of the Euro-zone.
Asada, T., Chen, P., Chiarella, C. & Flaschel, P. 2006, 'AD-AS and the Phillips curve: a baseline disequilibrium model' in Chiarella, C., Franke, R., Flaschel, P. & Semmler, W. (eds), Quantitative and Empirical Analysis of Nonlinear Dynamic Macromodels, Elsevier, Amsterdam, Netherlands, pp. 173-227.
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Chen, P., Chiarella, C., Flaschel, P. & Semmler, W. 2006, 'Keynesian Macrodynamics and the Phillips Curve. An Estimated Baseline Macromodel for the U.S. Economy'.
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In this paper we formulate a baseline disequilibrium AS-AD model and empirically estimate it with time series data for the
US-economy. The version of the model used here exhibits a Phillips-curve, a dynamic IS curve and a Taylor interest rate rule. It is based
on sticky wages and prices, perfect foresight of current inflation rates and adaptive expectations concerning the inflation climate in
which the economy operates. A version of Okun's law is used to link capacity utilization to employment. Our proposed nonlinear 5D model of
real market dynamics overcomes anomalies of the old Neoclassical synthesis and also the rational expectations methodology of the new
Neoclassical Synthesis. It resembles New Keynesian macroeconomics but permits nonclearing of markets. It exhibits typical Keynesian
feedback structures with asymptotic stability of its steady state for low adjustment speeds and with loss of stability { generally by way
of Hopf bifurcations { when certain adjustment speeds are made sufficiently large. We provide system estimates of our model, for quarterly
time series data of the U.S. economy 1965.1-2001.1, and study the stability features of the U.S. economy with respect to its various
feedback channels from an empirical perspective. Based on these estimates, which in particular imply that goods market dynamics are profit
led, we find that the dynamics are strongly convergent around the steady state, if monetary policy is sufficiently active, but will lose
this feature if the inflationary climate variable or the price inflation rate itself adjusts sufficiently fast. We also study to what
extent more active interest rate feedback rules or downward wage rigidity can stabilize the dynamics in the large when the steady state is
locally repelling. We study the economy's behavior due to faster adjustments. We find that monetary policy should allow for sufficient
steady state inflation in order to avoid stability problems in areas of the phase space w...
Chiarella, C., Flaschel, P., Franke, R. & Semmler, W. 2006, 'A high-dimensional model of real-financial market interaction: the cascade of stable matrices approach' in Chiarella, C., Franke, R., Flaschel, P. & Semmler, W. (eds), Quantitative and Empirical Analysis of Nonlinear Dynamic Macromodels, Elsevier, Amsterdam, Netherlands, pp. 359-384.
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Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. However, the impact of such dynamic phenomena on various statistical properties of the corresponding stochastic model, including skewness and excess kurtosis, various autocorrelation (AC) patterns of under and over reactions, and volatility clustering characterised by the long-range dependence of ACs, is not clear and has been very little studied. This paper aims to contribute to this issue. Through a simple behavioural asset pricing model with fundamentalists and chartists, we examine the statistical properties of the model and their connection to the dynamics of the underlying deterministic model. In particular, our analysis leads to some insights into various mechanisms that may generate some of the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data. © 2006 Springer-Verlag Berlin Heidelberg.
Chiarella, C., Flaschel, P., He, X. & Hung, H. 2006, 'A stochastic model of real-financial interaction with boundedly rational heterogeneous agents' in Chiarella, C., Franke, R., Flaschel, P. & Semmler, W. (eds), Quantitative and Empirical Analysis of Nonlinear Dynamic Macromodels, Elsevier, Amsterdam, Netherlands, pp. 333-358.
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A discrete-time dynamic model of a financial market is developed, where two types of agents, fundamentalists and chartists, allocate their wealth between two risky assets and a safe asset, according to one-period mean-variance maximization. The two groups of agents form different expectations about asset returns and their variance/covariance structure, and this results in different demand functions. At the end of each trading period, agents' demands are aggregated by a market maker, who sets the next period prices as functions of the excess demand. The model results in a high-dimensional nonlinear discrete-time dynamical system, which describes the time evolution of prices and agents' beliefs about expected returns, variances and correlation. It is shown that the unique steady state may become unstable through a Hopf-bifurcation and that an attracting limit cycle, or more complex attractors, exist for particular ranges of the key parameters. In particular, the two risky assets may exhibit "coupled" long-run price fluctuations and time-varying correlation of returns. © 2005 Springer-Verlag Berlin Heidelberg.
Chiarella, C. & He, X. 2005, 'An asset pricing model with adaptive heterogeneous agents and wealth effects' in Lux, T., Reitz, S. & Samanidou, E. (eds), Nonlinear Dynamics and Heterogeneous Interacting Agents, Springer, Berlin, Germany, pp. 269-285.
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The characterisation of agents' preferences by decreasing absolute risk aversion (DARA) and constant relative risk aversion (CRRA) are well documented in the literature and also supported in both empirical and experimental studies. This paper considers a financial market with heterogeneous agents having power utility functions, which are the only utility functions displaying both DARA and CRRA. By introducing a population weighted average wealth measure, we develop an adaptive model to characterise asset price dynamics as well as the evolution of population proportions and wealth dynamics. Some numerical simulations are included to illustrate the evolution of the wealth dynamics, market behaviour and market efficiency within the framework of heterogeneous agents.
Chiarella, C., Flaschel, P. & Semmler, W. 2004, 'Real-financial interaction: A reconsideration of the Blanchard model with a state-of-market dependent reaction coefficient', pp. 31-65.
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Chiarella, C. & He, X.Z. 2004, 'Dynamics of beliefs and learning under a(L)-processes - The homogeneous case', pp. 363-390.
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Chiarella, C., Dieci, R. & Gardini, L. 2003, 'A Dynamic Analysis of Speculation Across Two Markets'.
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A discrete time model of a financial market is proposed, where the time evolution of asset prices and wealth arises from the interaction of two groups of agents, fundamentalists and chartists.
Each group allocates its wealth between a risky asset (stock) and an alternative asset (bond), and the two groups have heterogeneous expectations about returns. We assume that chartists compute expected
returns by extrapolating past price changes, while fundamentalists form their expectations on the basis of their superior knowledge of fundamentals. Under the assumption that agents have CRRA utility,
investors' optimal demand for each asset depends on their wealth, and this results in growing price and wealth processes. The time evolution of the prices is modeled by assuming the existence of a market
maker, who sets excess demand of each asset to zero at the end of each trading period by taking an off-setting long or short position. The market maker is assumed to adjust the price, in each period,
partly on the basis of the excess demand and partly according to a particular market stabilization policy. The model is reduced to a high dimensional nonlinear discrete-time dynamical system with growing
prices and wealth. Although the model is nonstationary, suitable changes of variables lead to a stationary model where the dynamic variables are actual and expected returns, fundamental/price ratios, and
wealth proportions of chartists and fundamentalists. The steady states and other invariant sets of the model are determined, and important global dynamic phenomena are studied via numerical techniques.
Stochastic simulations are also performed, that show the ability of the model to generate some of the characteristic features of financial time series.
Chiarella, C., Szidarovszky, F. & Zhu, P.Y. 2002, 'The interaction of uncertainty and information lags in the Cournot oligopoly model', pp. 233-263.
Chiarella, C., Pasquali, S. & Runggaldier, W.J. 2002, 'On Filtering in Markovian Term Structure Models' in Yong, J. (ed), Recent Developments in Mathematical Finance, World Scientific, Singapore, pp. 139-150.
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Bhar, R., Chiarella, C. & Runggaldier, W. 2001, 'Estimation in Models of the Instantaneous Short Term Interest Rate By Use of a Dynamic Bayesian Algorithm'.
This paper considers the estimation in models of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the
instantaneous short rate of interest, we set up the stochastic dynamics for the discretely compounded market observed rates and propose a dynamic Bayesian estimation algorithm (i.e. a filtering algorithm)
for a time-discretised version of the resulting interest rate dynamics. The filter solution is computed via a further spatial discretization (quantization) and the convergence of the latter to its
continuous counterpart is discussed in detail. The method is applied to simulated data and is found to give a reasonable estimate of the conditional density function and to be not too demanding
computationally.
Chiarella, C., Flaschel, P., Franke, R. & Semmler, W. 2001, 'Output, Financial Markets & Growth. An Extension of the Balnchard Stock-Market Approach' in Friedman, R., Knuppel, L. & Lutkepohl, H. (eds), Econometric Studies: A Festschrift in Honour of Joachim Frohn, LIT Verlag, Munster, Germany, pp. 159-183.
Chiarella, C., Flaschel, P. & Semmler, W. 2001, 'The macrodynamics of debt deflation', pp. 133-184.
Chiarella, C. & Khomin, A. 2000, 'Learning in a Generalized Dornbusch Model of Exchange Rate Dynamics'.
In this paper we propose a framework for studying possible causes of excess exchange rate volatility. The
framework consists of a generalized Dornbusch model of exchange rate dynamics, involving imperfect substitutability
between assets, lagged nonlinear protfolio adjustment and les than perfectly rational expectations. As the model involves
non-linear portfolio adjustment, it remains globally bounded even when the steady state is locally unstable. This economic
environment is populated by a group of sophisticated agents who employ a maximum likelihood learning algorithm tolearnce
about the "true" model. We use simulations to study the convergence of the learning scheme and its effect on exchange rate
dynamics. Our analysis suggests that learning of speed of adjustment type parameters can be a source of exchange rate
bubbles because of their effect on the local stability of the steady state.
Chiarella, C. & Khomin, A. 2000, 'The dynamic interaction of rational fundamentalists and trend chasing chartists in a monetary economy', pp. 151-165.
Chiarella, C., Flaschel, P., Groh, G. & Semmler, W. 2000, 'AS-AD disequilibrium dynamics and economic growth' in Hartl, E.J., Dockner, R.F., Luptacik, M. & Sorger, G. (eds), Optimization, Dynamics, and Economic Analysis, Physica-Verlag, Heidelberg, Germany, pp. 101-117.
Chiarella, C. & Flaschel, P. 2000, 'The emergence of complex dynamics in a "naturally" nonlinear integrated Keynesian model of monetary growth', pp. 111-145.
Bhar, R. & Chiarella, C. 2000, 'Analysis of time varying exchange rate risk premia', pp. 255-273.
Chiarella, C. & Szidarovszky, F. 1999, 'The Birth of Limit Cycles in Nonlinear Oligopolies with Continuously Distributed Information Lags'.
The dynamic behaviour of the output in nonlinear oligopolies is examined when the equilibrium is locally
unstable. Continuously distributed time lags are assumed in obtaining information about "rivals" output as well as in
obtaining or implementing information about the firms' own output. The Hopf bifurcation theorem is used to find conditions
under which limit cycle motion is born. In addition to the classical Cournot model, labor managed and rent seeking
oligopolies are also investigated.
In this paper we investigate the dynamics of the traditional cobweb model where producres are risk averse and
seek to learn the distribution of asset prices. We consider the subjective estimates of the statistical distribution of
the market prices based on L-step backward time series of market clearing prices. With constant absolute risk aversion,
the cobweb model becomes nonlinear. Sufficient conditions on the local stability of the unique positive equilibrium of
the nonlinear model are derived and, consequently, we show that the local stability region is proportional to the lag
length L. When the equilibrium loses its local stability, we show that, for L = 2, the model has a strong 1:3 resonance
bifurcation and a family of fixed points of order 3 becomes unstable on both sides of criticality. For general lag
lengths, numerical simulations suggest that the model displays a variety of complex dynamics.
Conferences
© 2015 by De Gruyter. This paper reconsiders the popular Brock and Hommes [Brock, W. A., and C. H. Hommes. 1997. "A Rational Route to Randomness." Econometrica 65: 1059-1096.] framework for the study of the evolution of agents' choices when different behavioural strategies are available. In particular, we model the intensity of choice as an endogenous variable and not a parameter as it is commonly treated in the literature. We make use of the maximum entropy inference to obtain an analogous exponential type probability function for strategies, with the intensity of choice varying over time according to the performance of each strategy. We test this approach on an existing asset pricing model, highlighting the effects on the system of the different switching pattern that originate in the endogenous switching intensity.
By employing a continuous time multi-factor stochastic volatility model, the dynamic relation between returns and volatility in the commodity futures markets is analyzed. The model is estimated by using an extensive database of gold and crude oil futures and futures options. A positive relation in the gold futures market and a negative relation in the crude oil futures market subsist, especially over periods of high volatility principally driven by market-wide shocks. The opposite relation holds over quiet periods typically driven by commodity-specific effects. According to the proposed convenience yield effect, normal (inverted) commodity futures markets entail a negative (positive) relation.
Chiarella, C., Di Guilmi, C. & Zhi, T. 2014, 'Modelling the 'Animal Spirits' of Bank's Lending Behaviour', Society for Nonlinear Dynamics and Econometrics 22nd Annual Symposium, New York, USA.
Chiarella, C., Griebsch, S. & Kang, B. 2014, 'A comparative study on time-efficient methods to price compound options in the heston model', 8th World Congress of the Bachelier Finance Society, Brussels, Belgium.
Chiarella, C., Beyna, I. & Kang, B. 2014, 'Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time Dependent Volatility', 20th International Conference Computing in Economics and Finance, Oslo, Norway.
Chiarella, C., Griebsch, S. & Kang, B. 2014, 'A comparative study on time-efficient methods to price compound options in the Heston model', Fourth IMS-FPS (Institute for Mathematical Statistics - Finance, Probability and Statistics) Workshop, Sydney, Australia.
Chiarella, C., Griebsch, S. & Kang, B. 2014, 'A comparative study on time-efficient methods to price compound options in the Heston model', International Symposium on Di, Sanya, Hainan, China.
This paper analyses the volatility structure of commodity derivatives markets. The model encompasses hump-shaped, unspanned stochastic volatility, which entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for options on commodity futures. Using an extensive database of crude oil futures and futures options spanning 21. years, we find the presence of hump-shaped, partially spanned stochastic volatility in the crude oil market. The hump shaped feature is more pronounced when the market is more volatile, and delivers better pricing as well as hedging performance under various dynamic factor hedging schemes. © 2013 Elsevier B.V.
This article presents a continuous-time model of exchange rates not only relying on macroeconomic factors but also having an investor heterogeneity component. The driving macroeconomic factor is the domestic-foreign interest rate differential, while the investor heterogeneity is described by the expectations of boundedly rational portfolio managers who use a weighted average of the expectations of fundamentalists and chartists. Within this framework, the different roles of the macroeconomic factor and investor heterogeneity in the determination of the exchange rate are examined explicitly. We show that this simple model generates very complicated market behaviour, including the existence of multiple steady-state equilibria, deviations of the market exchange rate from the fundamental one and market fluctuations. Numerical simulation of the corresponding stochastic version of the model shows that the model is able to generate typical time series and volatility clustering patterns observed in exchange rate markets. © 2013 Copyright Taylor and Francis Group, LLC.
Chiarella, C. & Kang, B. 2013, 'The evaluation of American compound option prices under stochastic volatility and stochastic interest rates', JOURNAL OF COMPUTATIONAL FINANCE, pp. 71-92.
Chiarella, C. & Ziveyi, J. 2013, 'American option pricing under two stochastic volatility processes', Applied Mathematics and Computation, pp. 283-310.
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In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes as proposed in Christoffersen, Heston and Jacobs (2009) [13]. We consider the associated partial differential equation (PDE) for the option price and its solution. An integral expression for the general solution of the PDE is presented by using Duhamel's principle and this is expressed in terms of the joint transition density function for the driving stochastic processes. For the particular form of the underlying dynamics we are able to solve the Kolmogorov PDE for the joint transition density function by first transforming it to a corresponding system of characteristic PDEs using a combination of Fourier and Laplace transforms. The characteristic PDE system is solved by using the method of characteristics. With the full price representation in place, numerical results are presented by first approximating the early exercise surface with a bivariate log linear function. We perform numerical comparisons with results generated by the method of lines algorithm and note that our approach provides quite good accuracy. © 2013 Elsevier Inc. All rights reserved.
Chiarella, C., Kang, B. & Meyer, G. 2013, 'The evaluation of barrier option prices under stochastic volatility', The First Asian Quantitative Finance Conference, Singapore.
Chiarella, C., Kang, B. & Poon, S. 2013, 'Forward variance and VIX futures dynamics', 57th Annual Meeting of the Australian Mathematical Society, Sydney, Australia.
Chiarella, C., He, X.-.Z. & Wei, L. 2013, 'Learning and Evolution of Trading Strategies in Limit Order Markets'.
How do traders process and learn from market information, what trading strategies should they use, and how does learning affect the market? This paper proposes a learning model of an arti cial limit order market with asymmetric
information to address these issues. Using a genetic algorithm as a learning mechanism, we show that learning, in particular the learning from uninformed traders, improves market informational efficiency and has a significant impact on
the stylized facts of limit order markets, order submission, liquidity supply and consumption, the hump shaped order book near the quote, and the bid-ask spread. Moreover, the learning affects the evolution process of the trading
strategies for all traders. The model provides some insights into market efficiency, the interaction of traders, the dynamics of limit order books, and the evolution of trading strategies.
Chiarella, C., Kang, B. & Meyer, G.H. 2012, 'The evaluation of barrier option prices under stochastic volatility', Computers and Mathematics with Applications, pp. 2034-2048.
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This paper considers the problem of numerically evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Heston (1993) [7]. We develop a method of lines approach to evaluate the price as well as the delta and gamma of the option. The method is able to efficiently handle both continuously monitored and discretely monitored barrier options and can also handle barrier options with early exercise features. In the latter case, we can calculate the early exercise boundary of an American barrier option in both the continuously and discretely monitored cases. © 2012 Elsevier Ltd. All rights reserved.
Bao, Y., Chiarella, C. & Kang, B. 2012, 'Particle Filters for Markov Switching Stochastic Volatility Models'.
This paper proposes an auxiliary particle filter algorithm for inference in regime switching stochastic volatility models in which the regime state is governed by a first-order Markov chain. We
proposes an ongoing updated Dirichlet distribution to estimate the transition probabilities of the Markov chain in the auxiliary particle filter. A simulation-based algorithm is presented for the method
which demonstrated that we are able to estimate a class of models in which the probability that the system state transits from one regime to a different regime is relatively high. The methodology is
implemented to analyze a real time series: the foreign exchange rate of Australian dollars vs South Korean won.
Chiarella, C., Clewlow, L. & Kang, B. 2011, 'The evaluation of gas swing contracts with regime switching', Topics in Numerical Methods for Finance: Proceedings in Mathematics and Statistics, Numerical Methods for Finance Conference 2011, Springer, Limerick, Ireland, pp. 155-176.
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Chiarella, C. 2012, 'The difference between Europe and the rest of the world - An Australian perspective', First Meeting of COST working groups Action IS1104, Urbino, Italy.
Chiarella, C., Dieci, R. & He, X. 2012, 'Time-varying beta: A boundedly rational equilibrium approach', Seminar Presentatiom, National Cheng-Chi University, Taiwan.
Chiarella, C., Dieci, R. & He, X. 2012, 'Heterogeneity, market mechanisms, and asset price dynamics', First Meeting of COST working groups Action IS1104, Urbino, Italy.
Chiarella, C. & Di Guilmi, C. 2012, 'A reconsideration of the formal Minskyan analysis: Microfoundations, endogenous money and the public sector', MDEF2012, Urbino, Italy.
Beyna, I., Chiarella, C. & Kang, B. 2012, 'Pricing interest rate derivatives in a multifactor HJM model with time dependent volatility', SIAM Conference on Financial Mathematics and Engineering, Minneapolis, Minnesota, USA.
Chiarella, C. & Kang, B. 2012, 'The evaluation of American compound option prices under stochastic volatility and stochastic interest rates', 7th World Congress of the Bachelier Finance Society, Sydney, Australia.
Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', 18th International Conference Computing in Economics and Finance, Prague, Czech Republic.
Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', 29th Spring International Conference of the French Finance Association, Strasbourg, France.
Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', Seminar Presentation, University of Cyprus, Cyprus.
Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', Asian Finance Association and Taiwan Finance Association 2012 Joint International Conference, Taipei, Taiwan.
Bohm, V., Chiarella, C., He, X. & Huls, T. 2012, 'A homoclinic route to volatility: Dynamics of asset prices under autoregressive forecasting', Seminar Presentation, Tunghai University, Taiwan.
Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This papers incorporates the adaptive behaviour of agents with heterogeneous beliefs and establishes
an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behaviour of agents switching to better performing trading strategies can cause large deviations of the market price from
the fundamental value of one asset to spill over to other assets. Also, this spill-over effect is associated with high trading volumes and persistent volatility characterized by significantly decaying autocorrelations of, and positive
correlation between, price volatility and trading volume.
Chiarella, C., Kang, B. & Meyer, G. 2012, 'The evaluation of barrier option prices under stochastic volatility', Seminar Presentation, Department of Mathematics, Zhejiang University, Hangzhou, China.
Chiarella, C., Kang, B. & Nikitopoulos Sklibosios, C. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence', Seminar Presentation, Sydney Institute of Language and Commerce, Shanghai University, Shanghai, China.
Chiarella, C., Kang, B. & Nikitopoulos Sklibosios, C. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence"', Seminar Presentation, School of Commerce and the Centre for Applied Financial Studies, University of South Australia, Adelaide, Australia.
Chiarella, C., Hsiao, C.-.Y. & To, T.-.D. 2011, 'Stochastic Correlation and Risk Premia in Term Structure Models'.
This paper proposes and analyses a term structure model that allows for both stochastic correlation between underlying factors and an extended market price of risk specification. The issues of
invariant transformation and different normalization are then considered so that a comparison between different restrictions can be made. We show that significant improvement in bond fitting is obtained by
both allowing the market price of risk to have an extended affine form, and allowing the correlation between underlying factors to be stochastic as well as of variable sign. The overall model fit is more
negatively impacted by the restriction on the market price of risk than the restriction of correlated factors. However, the stochastic correlation is priced significantly by market participants, though its
impact on the risk premia reduces gradually as time to maturity increases. In addition, stochastic correlation is vital in obtaining good hedged portfolio positions. Certainly, the best hedged portfolio is
the one that is built based on the model that takes into account both stochastic correlation and extended market price of risk.
Chiarella, C., Hsiao, C. & To, T. 2011, 'Stochastic correlation and risk premia in term structure models', Seminar Presentation, Copenhagen Business School, Copenhagen, Denmark.
Chiarella, C., Dieci, R. & He, X. 2011, 'Time-varying beta: A boundedly rational equilibrium approach', Seminar Presentation, University of Freiburg, Germany.
Chiarella, C., Dieci, R. & He, X. 2011, 'Time-varying beta: A boundedly rational equilibrium approach', Seminar Presentation, Dublin City University, Ireland.
Chiarella, C. & Kang, B. 2011, 'The evaluation of American compound option prices under stochastic volatility and stochastic interest rates', 17th International Conference on Computing in Economics and Finance, San Francisco, California, USA.
Chiarella, C., Benya, I. & Kang, B. 2011, 'Pricing interest rate derivatives in a multifactor HJM model with time dependent volatility', 55th Annual Meeting of the Australian Mathematical Society, Wollongong, Australia.
Chiarella, C., Benya, I. & Kang, B. 2011, 'Pricing interest rate derivatives in a multifactor HJM model with time dependent volatility', Seminar Presentation, Tongji University, Shanghai, China.
Chiarella, C., Benya, I. & Kang, B. 2011, 'Pricing interest rate derivatives in a multifactor HJM model with time dependent volatility', Quantitative Methods in Finance 2011 Conference, Sydney Australia.
Chiarella, C., Hsiao, C. & To, T. 2010, 'Risk premia and Wishart term structure models', Society for Nonlinear Dynamics and Econometrics 18th Annual Symposium, Novara, Italy.
Chiarella, C., He, X. & Zheng, M. 2010, 'The market impact and survival of boundedly rational traders', Young Researchers Workshop in Finance, Tokyo, Japan.
Chiarella, C., Giansante, S., Sordi, S. & Vercelli, A. 2010, 'Financial fragility and interacting units: An exercise', New Economic Windows, pp. 117-126.
This paper assumes that financial fluctuations are the result of the dynamic interaction between liquidity and solvency conditions of individual financial units. The framework is designed as a heterogeneous agent model which proceeds through discrete time steps within a finite time horizon. The interaction at the microlevel between financial units and the market maker, who is in charge of clearing the market, produces interesting complex dynamics. The model is analyzed by means of numerical simulations and agent-based computational economics (ACE) approach. The behaviour and evolution of financial units are studied for different parameter regimes in order to show the importance of the parameter setting in the emergence of complex dynamics. Monetary policy implications for the banking sector are also discussed. © Springer-Verlag Italia 2010.
Chiarella, C. & Di Guilmi, C. 2010, 'Debt deflation dynamics in a heterogenous agent economy', 16th International Conference on Computing in Economics and Finance, London, UK.
Chiarella, C., Clewlow, L. & Kang, B. 2010, 'The evaluation of swing contracts with regime switching', 16th International Conference on Computing in Economics and Finance, London, UK.
Chiarella, C., Clewlow, L. & Kang, B. 2010, 'The evaluation of swing contracts with regime switching', 6th World Congress of the Bachelier Finance Society, Toronto, Canada.
Chiarella, C., Kang, B. & Meyer, G. 2010, 'The evaluation of barrier option prices under stochastic volatility', 6th World Congress of the Bachelier Finance Society, Toronto, Canada.
Chiarella, C. & Ziveyi, J. 2010, 'American option pricing under two stochatsic volatility processes', 6th World Congress of the Bachelier Finance Society, Toronto, Canada.
Chiarella, C., Clewlow, L. & Kang, B. 2010, 'Modelling and estimating the forward price curve in the energy market', Symposium on Challenges in Commodity-Energy Price and Revenue Management, Heidelberg, Germany.
Chiarella, C., Clewlow, L. & Kang, B. 2010, 'The evaluation of swing contracts with regime switching', 24th European Conference on Operations Research, Lisbon, Portugal.
Chiarella, C., Hsiao, C. & To, T. 2010, 'Risk premia and Wishart term structure models', China International Conference in Finance, Beijing, China.
Chiarella, C. & Maina, S.C. 2010, 'Defaultable hidden Markov HJM term structure class of models', 16th International Conference on Computing in Economics and Finance, London, UK.
Chiarella, C., Clewlow, L. & Kang, B. 2010, 'The evaluation of swing contracts with regime switching', Quantitative Methods in Finance 2010 Conference, Sydney, Australia.
Novikov, A. & Chiarella, C. 2009, 'Contemporary Quantitative Finance, Essays in Honour of Eckhard Platen', Quantitative Mathematical Finance, Quantitative Mathematical Finance, Springer, Sydney, Australia, pp. 1-410.
The contributors to this volume write a series of articles outlining contemporary advances in a number of key areas of mathematical finance such as, optimal control theory applied to finance, interest rate models, credit risk and credit derivatives, use of alternative stochastic processes, numerical solution of equations of mathematical finance, estimation of stochastic processes in finance. The list of authors includes many of the researchers who have made the major contributions to these various areas of mathematical finance. This volume addresses both researchers and professionals in financial institutions, as well as regulators working in the above mentioned fields.
Chiarella, C., Hung, H. & To, T.-.D. 2009, 'The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach', COMPUTATIONAL STATISTICS & DATA ANALYSIS, pp. 2075-2088.
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Giansante, S., Chiarella, C., Sordi, S. & Cercelli, A. 2009, 'Financial fragility and fluctuations in a world with multi-heterogeneous agents', Workshop on the Complexity of Financial Crisis in a Long-Period Perspective: Facts, Theory and Models, Sienna, Italy.
Chiarella, C., Clewlow, L. & Kang, B. 2009, 'Modelling and Estimating the Forward Price Curve in the Energy Market'.
The stochastic or random nature of commodity prices plays a central role in models for valuing financial contingent claims on commodities. In this paper, by enhancing a multifactor framework which
is consistent not only with the market observable forward price curve but also the volatilities and correlations of forward prices, we propose a two factor stochastic volatility model for the evolution of
the gas forward curve. The volatility is stochastic due to a hidden Markov Chain that causes it to switch between "on peak" and "off peak" states. Based on the structure functional forms for the volatility,
we propose and implement the Markov Chain Monte Carlo (MCMC) method to estimate the parameters of the forward curve model. Applications to simulated data indicate that the proposed algorithm is able to
accommodate more general features, such as regime switching and seasonality. Applications to the market gas forward data shows that the MCMC approach provides stable estimates.
Chiarella, C., Clewlow, L. & Kang, B. 2009, 'Pricing swing options and modelling multi-factor forward price curves in the energy market', Research Forum on Finance and Decision Making, Tokyo, Japan.
Chiarella, C., He, X. & Zheng, M. 2009, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs', AsianFA International Conference, Brisbane, Australia.
Chiarella, C., He, X. & Zheng, M. 2009, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs', International Conference on Economic Science with Heterogeneous Interacting Agents, Beijing, China.
Chiarella, C., Kang, B., Meyer, G.H. & Ziogas, A. 2009, 'The evaluation of american option prices under stochastic volatility and jump-diffusion dynamics using the method of lines', International Journal of Theoretical and Applied Finance, pp. 393-425.
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This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston [18], and by a Poisson jump process of the type originally introduced by Merton [25]. We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer [26] for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen and Toivanen [21]. The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation and which is taken as the benchmark for the price. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered. © 2009 World Scientific Publishing Company.
Chiarella, C. & Kang, B. 2009, 'The Evaluation of American Compound Option Prices Under Stochastic Volatility Using the Sparse Grid Approach'.
A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we demonstrate a
partial differential equation (PDE) approach to pricing American-type compound options where the underlying dynamics follow Heston's stochastic volatility model. This price is formulated as the solution
to a two-pass free boundary PDE problem. A modified sparse grid approach is implemented to solve the PDEs, which is shown to be accurate and efficient compared with the results from Monte Carlo simulation
combined with the Method of Lines.
Chiarella, C. & Kang, B. 2009, 'The evaluation of American compound option prices under stochastic volatility using the sparse grid approach', 3rd Workshop on High-Dimensional Approximation, Sydney, Australia.
Chiarella, C., He, X. & Zheng, M. 2009, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs', 15th International Conference on Computing in Economics and Finance, Sydney, Australia.
Chiarella, C., Dieci, R. & He, X. 2009, 'Time-varying beta: A bounded rational equlibrium approach', Evolution and Market Behavior in Economics and Finance Workshop, Pisa, Italy.
Chiarella, C., Hsiao, C. & To, T. 2009, 'Risk premia in dynamic affine term structure models', Young Statistician Conference, Sydney, Australia.
Chiarella, C., Dieci, R. & He, X. 2009, 'Time-varying beta: A bounded rational equilibrium approach', Seminar Presentation, Bocconi University, Milan, Italy.
Chiarella, C., Clewlow, L. & Kang, B. 2009, 'Modelling and estimating the forward price curve in the energy market', Seminar Presentation, Universita dell' Insubria, Varese, Italy.
Chiarella, C. 2009, 'Heterogeneity, market mechanisms and asset price dynamics', Financial Econometrics Workshop on Informational Asymmetry/ Heterogeneous Beliefs, Auckland, New Zealand.
Chiarella, C. & Flaschel, P. 2009, 'The complex dynamics of capitalism', Workshop on Nonlinearity, Complexity and Randomness, Trento, Italy.
Chiarella, C., Clewlow, L. & Kang, B. 2009, 'Modelling and estimating the forward price curve in the energy market', 3rd International Conference on Computational and Financial Econometrics, Limassol, Cyprus.
Chiarella, C. & Di Guilmi, C. 2009, 'Financial instability hypothesis: A stochastic microfoundation framework', The Sixth International Workshop on Agent-based Approaches in Economic and Social Complex Systems, Taipei, Taiwan.
Chiarella, C. & Di Guilmi, C. 2009, 'Financial instability hypothesis: A stochastic microfoundation framework', 8th Annual Meeting of the European Economics and Finance Society International Conference, Warsaw, Poland.
Chiarella, C. & Huang, N. 2009, 'Modelling default correlations in a two-firm model by dynamic leverage ratios following jump diffusion processes', Seminar Presentation, Discipline of Operations Management and Econometrics, University of Sydney, Sydney, Australia.
Bohm, V., Chiarella, C. & He, X. 2008, 'Dynamics of asset prices in the CAPM under autoregressive forecasting and noise', International Workshop on Nonlinear Economic Dynamics and Financial Market Modelling, Beijing, China.
Bohm, V., Chiarella, C. & He, X. 2008, 'Dynamics of asset prices in the CAPM under autoregressive forecasting and noise', MDEF 2008, Urbino, Italy.
Chiarella, C. 2008, 'The evaluation of American compound option prices under stochastic volatility', 5th International Conference on Computational Management Science, London, UK.
Chiarella, C., He, X. & Zheng, M. 2008, 'Consensus investor and intertemporal asset pricing with heterogeneous beliefs', International Workshop on Nonlinear Economic Dynamics and Finance, Beijing, China.
Chiarella, C., Clewlow, L. & Kang, B. 2008, 'The evaluation of swing option price with make-up and carry-forward provisions', Bachelier Finance Society 5th World Congress, London, UK.
Chiarella, C., Dieci, R. & He, X. 2008, 'Heterogeneity, market mechanisms and asset price dynamics', Learning Week, Summer Workshop, Federal Reserve Bank of St Louis, St Louis, USA.
Chiarella, C., He, X. & Zheng, M. 2008, 'Heterogeneous expectations and exchange rate dynamics', 14th International Conference on Computing in Economics and Finance, Paris, France.
Chiarella, C., He, X. & Zheng, M. 2008, 'The stochastic dynamics of speculative prices', Bachelier Finance Society 5th World Congress, London, UK.
Chiarella, C. & Kang, B. 2008, 'The evaluation of American compound option prices under stochastic volatility', 2nd Annual Risk Management Conference, Singapore.
Chiarella, C., Dieci, R. & He, X. 2008, 'A dynamic heterogeneous beliefs CAPM', Modelling Dynamics in Economics and Finance MDEF 08, Urbino, Italy.
Chiarella, C. & Kang, B. 2008, 'The evaluation of American compound option prices under stochastic volatility', Seminar Presentation, University of Karlsruhe, Karlsruhe, Germany.
Chiarella, C. & Kang, B. 2008, 'The evaluation of American compound option prices under stochastic volatility', 14th International Conference of the Society for Computational Economics, Paris, France.
Chiarella, C. 2008, 'The evaluation of American compound option prices under stochastic volatility', Second Annual Risk Management Conference, Singapore.
Chiarella, C., Dieci, R. & He, X. 2008, 'Heterogeneity, market mechanisms and asset price dynamics', Seminar Presentation, University of Karlsruhe, Karlsruhe, Germany.
Chiarella, C., He, X. & Zheng, M. 2008, 'Consensus Investor and Intertemporal Asset Pricing with Heterogeneous Beliefs', Quantitative Methods in Finance 2008 Conference, Sydney, Australia.
Chiarella, C. 2008, 'The evaluation of swing options with make-up and carry-forward provisions', Quantitative Methods in Finance 2008 Conference, Sydney, Australia.
Chiarella, C., He, X. & Zheng, M. 2008, 'Heterogeneous expectations and exchange rate dynamics', International Workshop on Nonlinear Economic Dynamics and Financial Market Modelling, Beijing, China.
Chiarella, C., He, X. & Zheng, M. 2008, 'Heterogeneous expectations and exchange rate dynamics', Seminar Presentation, Sydney Agents Network, Sydney, Australia.
Giansante, S., Chiarella, C., Sordi, S. & Vercelli, A. 2008, 'Financial fragility and fluctuations in a world with multi-heterogeneous agents', MDEF 2008, Urbino, Italy.
Chiarella, C., He, X., Wang, D. & Zhu, M. 2008, 'Stock price and market maker inventory dynamics with heterogeneous beliefs', International Workshop on Nonlinear Dynamics and Financial Market Modelling, Beijing, China.
Thulasiram, R.K., Downing, C.T., Chiarella, C., Coleman, T., Dempster, M., Dongarra, J., Duan, J.-.C., Gao, G., Appadoo, S.S., Atiya, A., Bagchi, A., Birge, J., Brabazon, A., Broadie, M., Campolieti, J., Cincotti, S., Downing, C., Gilli, M., Isaenko, S., Jacoby, G., Kumar, K., Klebaner, F., Li, X., Li, Y., Livdan, D., Lyuu, Y.-.D., Nath, G.C., Okten, G., Oosterlee, C.W., Ouskel, A.M., Platen, E., Seco, L., Srinivasan, A., Srinivasan, R., Thenmozhi, M., Thulasiraman, P., Tsang, E.P.K., Wagner, A., Wang, L., Wilson, C., Wittum, G., Ing, C.W. & Tanaka-Yamawaki, M. 2008, 'Message from PDCoF-08 Workshop Chairs', IPDPS Miami 2008 - Proceedings of the 22nd IEEE International Parallel and Distributed Processing Symposium, Program and CD-ROM.
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The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t, T) cause jumps and defaults to the defaultable bond prices Pd(t, T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realizations in terms of benchmark defaultable forward rates. In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications. © World Scientific Publishing Company.
The defaultable forward rate is modelled as a jump diffusion process within the Schönbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t,T) cause jumps and defaults to the defaultable bond prices Pd(t,T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realizations in terms of benchmark defaultable forward rates. In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications.
Adolfsson, T., Cheang, G.H., Chiarella, C. & Ziogas, A. 2007, 'Approximate evaluation of European spread options under jump-diffusion dynamics', 13th International Conference on Computing in Economics and Finance, Montreal, Canada.
Chiarella, C. 2007, 'The stochastic dynamics of speculative behaviour', Workshop on Statistical Physics and Financial Markets, Trieste, Italy.
Chiarella, C. 2007, 'Pricing American options under stochastic volatility', Convegno Amases, Leccie, Italy.
Chiarella, C., He, X. & Zheng, M. 2007, 'The stochastic price dynamics of speculative behaviour', 13th International Conference on Computing in Economics and Finance, Montreal, Canada.
Chiarella, C. & Hsiao, C. 2007, 'Optimal investment strategies under stochastic volatility', 13th International Conference on Computing in Economics and Finance, Montreal, Canada.
Chiarella, C., Dieci, R. & He, X. 2007, 'Aggregation of heterogeneous beliefs and asset pricing theory: A mean-variance analysis', ASFA/FMA Conference, Hong Kong, China.
Within the framework of the heterogeneous agent paradigm, we establish a stochastic model of speculative price dynamics involving of two types of agents, fundamentalists and chartists, and the
market price equilibria of which can be characterised by the invariant measures of a random dynamical system. By conducting a stochastic bifurcation analysis, we examine the market impact of speculative
behaviour. We show that, when the chartists use lagged price trends to form their expectations, the market equilibrium price can be characterised by a unique and stable invariant measure when the activity
of the speculators is below a certain critical value. If this threshold is surpassed, the market equilibrium can be characterised by more than two invariant measures, of which one is completely stable,
another is completely unstable and the remaining ones may exhibit various types of stability. Also, the corresponding stationary measure displays a significant qualitative change near the threshold value.
We show that the stochastic model displays behaviour consistent with that of the underlying deterministic model. However, when the time lag in the formation of the price trends used by the chartists
approaches zero, such consistency breaks down. In addition, the change in the stationary distribution is consistent with a number of market anomalies and stylised facts observed in financial markets,
including a bimodal logarithmic price distribution and fat tails.
Cheang, G.H., Chiarella, C., Meyer, G. & Ziogas, A. 2006, 'The valuation of American spread options under jump-diffusion processes', Bachelier Finance Society 4th World Congress, Tokyo, Japan.
Cheang, G.H., Chiarella, C. & Ziogas, A. 2006, 'American-style options on two assets under jump-diffusion processes', Bachelier Finance Society 4th World Congress, Tokyo, Japan.
Chen, P., Chiarella, C., Flaschel, P. & Hung, H. 2006, 'Keynesian Disequilibrium Dynamics: Convergence, Roads to Instability and the Emergence of Complex Business Fluctuations'.
We reformulate the traditional AS-AD growth model of the Neoclassical Synthesis (stage I) with a Taylor policy rule replacing the
conventional LM-curve, with gradually adjusting wages as well as prices, and with perfect foresight on current inflation rates and an
adaptively revised notion of an inflationary climate in which the economy is operating. We compare this approach with the New Keynesian
approach, the Neoclassical Synthesis, stage II, with staggered price and wage setting and find various common components, yet with
radically different dynamic implications due to our treatment of the forward-looking part of our wage-price spiral. We show for a system
estimate of our model that it implies qualitatively local asymptotic stability and when its estimated form is simulated in response to
isolated shocks strongly damped business fluctuations, due to a stable interaction of goods market dynamics with the interest rate policy
of the central bank and due to a normal working of a real-wage feedback chain. These results are however endangered – leading in fact to
economic breakdown – when there is a global floor to money wage inflation rates. In this case, the return of some money wage flexibility
in deep depressions is of help in restoring viability of the model, thereby even avoiding explosive dynamics and the collapse of the
economy. This situation leads to viable, but complex business fluctuations.
Chiarella, C., Dieci, R. & He, X. 2006, 'A dynamic heterogenous beliefs CAPM', Workshop on Financial Market Dynamics, Piacenza, Italy.
Chiarella, C., Dieci, R. & He, X.-.Z. 2006, 'Aggregation of Heterogeneous Beliefs and Asset Pricing Theory: A Mean-Variance Analysis'.
Within the standard mean-variance framework, this paper provides a procedure to aggregate the heterogeneous beliefs in not only risk preferences and expected payoffs but also variances/covariances
into a market consensus belief. Consequently, an asset equilibrium price under heterogeneous beliefs is derived. We show that the market aggregate behavior is in principle a weighted average of
heterogeneous individual behaviors. The CAPM-like equilibrium price and return relationships under heterogeneous beliefs are obtained. The impact of diversity of heterogeneous beliefs on the market
aggregate risk preference, asset volatility, equilibrium price and optimal demands of investors is examined. As a special case, our result provides a simple explanation for the empirical relation between cross-sectional
volatility and expected returns.
Chiarella, C., Dieci, R. & He, X. 2006, 'On the dynamic behavior of asset prices in disequilibrium: Where are we after three decades?', MDEF 2006, Urbino, Italy.
Chiarella, C., Dieci, R. & He, X. 2006, 'On the dynamic behaviour of asset prices in disequilibrium: Where are we after three decades?', WIVA 3 Conference, Sienna, Italy.
Chiarella, C., He, X. & Li, Y. 2006, 'A dynamic heterogenous beliefs CAPM', 1st International Conference on Economic Science with Heterogenous Interacting Agents, Bologna, Italy.
Chiarella, C. & Gao, S. 2006, 'Direct estimation of a continous time model of the stock market', 14th IFAC Symposium on System Identification, Newcastle, Australia.
Chiarella, C., Meyer, G. & Ziogas, A. 2006, 'Pricing American options under stochastic volatility and jump-diffusion dynamics', Bachelier Finance Society 4th World Congress, Tokyo, Japan.
Chiarella, C., Meyer, G. & Ziogas, A. 2006, 'Pricing American options under stochastic volatility and jump-diffusion dynamics', Quantitative Methods in Finance 2006 Conference, Quantitative Methods in Finance 2006 Conference, Sydney, Australia.
Chiarella, C. & Ziogas, A. 2006, 'Pricing American options under stochastic volatility', Advanced Mathematical Methods for Finance Workshop, Advanced Mathematical Methods for Finance Workshop, Paris, France.
Perello, J., Iori, G. & Chiarella, C. 2006, 'Heterogenous trading rules impact on the microstructure of double auction markets', Complex Behavior in Economics: Modelling, Computing and Mastering Compexity, Complex Behavior in Economics: Modelling, Computing and Mastering Compexity, Aix-Enl Provence, France.
Chiarella, C. & Ziogas, A. 2005, 'Evaluation of American strangles', JOURNAL OF ECONOMIC DYNAMICS & CONTROL, pp. 31-62.
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Bohm, V. & Chiarella, C. 2005, 'Mean variance preferences expectations formation and the dynamics of random asset prices', MATHEMATICAL FINANCE, pp. 61-97.
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Chiarella, C. & Ziogas, A. 2005, 'Pricing American Options on Jump-Diffusion Processes using Fourier Hermite Series Expansions'.
This paper presents a numerical method for pricing American call options where the underlying asset price follows a jump-diffusion process. The method is based on the Fourier-Hermite series
expansions of Chiarella, El-Hassan & Kucera (1999), which we extend to allow for Poisson jumps, in the case where the jump sizes are log-normally distributed. The series approximation is applied to both
European and American call options, and algorithms are presented for calculating the option price in each case. Since the series expansions only require discretisation in time to be implemented, the
resulting price approximations require no asset price interpolation, and for certain maturities are demonstrated to produce both accurate and efficient solutions when compared with alternative methods,
such as numerical integration, the method of lines and finite difference schemes.
Chen, P., Chiarella, C., Flaschel, P. & Semmler, W. 2005, 'Keynesian dynamics and the wage-price spiral: Estimating and analysing a baseline disequilibrium approach', 11th Annual Conference on Computing in Economics and Finance, 11th Annual Conference on Computing in Economics and Finance, Society of Computational Economics, Washington, USA, pp. 1-53.
Chen, P., Chiarella, C., Flaschel, P. & Semmler, W. 2005, 'Keynesian dynamics and the wage-price spiral: Estimating and analysing a baseline disequilibrium approach', 13th Annual Symposium of the Society for Non-Linear Dynamics and Econometrics, 13th Annual Symposium of the Society for Non-Linear Dynamics and Econometrics, -, London, UK.
Chiarella, C., Cheang, G.H. & Ziogas, A. 2005, 'The valuation of multiple asset American options under jump diffusion processes', Mini Symposium on Financial Engineering, Mini Symposium on Financial Engineering, -, Kyoto, Japan.
Chiarella, C., Bohm, V. & He, X. 2005, 'The interaction of non-linear and stochastic elements in a one period model of asset price dynamics', Econophysics Colloquium, Econophysics Colloquium, -, Canberra, Australia.
Chiarella, C., Hsiao, C. & Semmler, W. 2005, 'Intertemporal asset allocation with inflation - indexed bonds', 11th Annual Conference on Computing in Economics and Finance, 11th Annual Conference on Computing in Economics and Finance, -, Washington, USA.
Chiarella, C. & Iori, G. 2005, 'The impact of heterogeneous trading rules of the limit', 13th Annual Symposium of the Society for Non-Linear Dynamics and Econometrics, 13th Annual Symposium of the Society for Non-Linear Dynamics and Econometrics, -, London, UK.
Chiarella, C. & Szidarovszky, F. 2005, 'The complex asymptotic behavior of dynamic oligopolies with partially cooperating firms', 4th Conference on Nonlinear Economic Dynamics, 4th Conference on Nonlinear Economic Dynamics, -, Urbino, Italy.
Chiarella, C. & Ziogas, A. 2005, 'Pricing American options under stochastic volatility', 11th Annual Conference on Computing in Economics and Finance, 11th Annual Conference on Computing in Economics and Finance, Society for Computational Economics, Washington, USA, pp. 1-36.
Chiarella, C. & Ziogas, A. 2005, 'Pricing American options on jump-diffusion processes: A numerical integration approach', Quantitative Methods in Finance 2005, Quantitative Methods in Finance 2005, -, Sydney, Australia.
Chiarella, C. & Ziogas, A. 2005, 'Pricing American options under stochastic volatility', Daiwa Securities International Workshop on Financial Engineering, Daiwa Securities International Workshop on Financial Engineering, -, Tokyo, Japan.
Hsiao, C., Semmler, W. & Chiarella, C. 2005, 'Intertemporal asset allocation when the underlying factors are unobservable', 13th Annual Symposium of the Society for Nonlinear Dynamics and Econometrics, 13th Annual Symposium of the Society for Nonlinear Dynamics and Econometrics, -, London, UK.
Chiarella, C., Hung, H. & To, T.-.D. 2005, 'The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach'.
This paper considers the dynamics for interest rate processes within a multi-factor Heath, Jarrow and Morton (1992) specification. Despite the flexibility of and the notable advances in
theoretical research about the HJM models, the number of empirical studies is still inadequate. This paucity is principally because of the difficulties in estimating models in this class, which are not
only high-dimensional, but also nonlinear and involve latent state variables. This paper treats the estimation of a fairly broad class of HJM models as a nonlinear filtering problem, and adopts the
local linearization filter of Jimenez and Ozaki (2003), which is known to have some desirable statistical and numerical features, to estimate the model via the maximum likelihood method. The estimator
is then applied to the interbank offered-rates of the U.S, U.K, Australian and Japanese markets. The two-factor model, with the factors being the level and the slope effect, is found to be a reasonable
choice for all of the markets. However, the contribution of each factor towards overall variability of the interest rates and the financial reward each factor claims differ considerably from one market to
another.
To, T., Chiarella, C. & Hung, H. 2005, 'The volatility structure of the fixed income market under the HJM framework: A non-linear filtering approach', The First Symposium on Econometric Theory and Its Applications, The First Symposium on Econometric Theory and Its Applications, -, Taipei, Taiwan.
Chiarella, C. & Ziogas, A. 2004, 'McKean's Methods Applied to American Call Options on Jump-Diffusion Processes'.
In this paper we derive the implicit integral equation for the price of an American call option in the case where the underlying asset follows a jump-diffusion process. We extend McKean's
incomplete Fourier transform approach to solve the free boundary problem under Merton's framework, with the distribution for the jump size remaining unspecified. We show how our results are consistent
with those of Gukhal (2001), who derived the same integral equation using the Geske-Johnson discretisation approach. The paper also derives some results concerning the limit for the free boundary
at expiry, and presents an iterative numerical algorithm for solving the linked integral equation system for the American call's price and early exercise boundary. This scheme is applied to Merton's
jump-diffusion model, where the jumps are log-normally distributed.
Chiarella, C. & Nikitopoulos-Sklibosios, C. 2004, 'A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework'.
This paper considers a class of term structure models that is a parameterisation of the Shirakawa (1991) extension of the Heath, Jarrow and Morton (1992) model to the case of jump-diffusions. We
consider specific forward rate volatility structures that incorporate state dependent Wiener volatility functions and time dependent Poisson volatility functions. Within this framework, we discuss the
Markovianisation issue, and obtain the corresponding affine term structure of interest rates. As a result we are able to obtain a broad tractable class of jump-diffusion term structure models. We
relate our approach to the existing class of jump-diffusion term structure models whose starting point is a jump-diffusion process for the spot rate. In particular we obtain natural jump-diffusion
versions of the Hull and White (1990, 1994) one-factor and two-factor models and the Ritchken and Sankarasubramanian (1995) model within the HJM framework. We also give some numerical simulations to gauge
the effect of the jump-component on yield curves and the implications of various volatility specifications for the spot rate distributions.
Chiarella, C. 2004, 'The time varying conditional distribution of the ex-ante equity risk premium implied by earnings and dividend yield', French Finance Association Meeting, French Finance Association Meeting, -, Paris, France.
Chiarella, C. 2004, 'A class of stochastic volatility HJM interest rate models', European financial management association meeting, European Financial Managment Association Meeting, -, Basel, Switzerland.
Chiarella, C. 2004, 'Mean variance preferences expectations formation and the dynamics of ransom asset prices', -, Quantitative Methods in Finance 2004 Conference, -, Sydney, Australia.
Chiarella, C., Dieci, R. & Gardini, L. 2004, 'Asset price and wealth dynamics in a financial market with heterogeneous agents', Computational Economics - 10th International Conference on Computing in Economics and Finance, Computational Economics - 10th International Conference on Computing in Economics and Finance, Society for Computational Economics, Amsterdam, Netherland, pp. 1-30.
Chiarella, C., Flaschel, P., He, X. & Hung, H. 2004, 'A stochastic model of real-financial interaction with boundedly rational heterogeneous agents', Society for nonlinear dynamics and economics, Society for Nonlinear Dynamics and Economics, -, Atlanta, USA.
The use of various moving average rules remains popular with financial market practitioners. These rules have recently
become the focus of a number empirical studies, but there have been very few studies of financial market models where
some agents employ technical trading rules also used in practice. In this paper we propose a dynamic financial market
model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is
governed by the difference between current price and a (long run) moving average. Both types of traders are boundedly
rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy
with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying
deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the
lag lengths used for the moving averages. By increasing the intensity of choice to switching strategies, we then examine
various rational routes to randomness for different moving average rules. The price dynamics of the moving average rule
is also examined and one of our main findings is that an increase of the window length of the moving average rule can
destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the
corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden
market crashes, price resistance and price switching between different levels.
Chiarella, C. & Iori, G. 2004, 'The microstructure of double auction markets: Some further simulation analysis', 3rd International conference on non-linear economic dynamics, 3rd International Conference on Nonlinear Economic Dynamics, -, Tokyo, Japan.
Chiarella, C. & Iori, G. 2004, 'The impact of heterogeneous trading rules on returns, volatility and the limit order book', Volatility of financial markets: theoretical models, forecasting and trading, Volatility of Financial Markets: Theoretical Models, Forecasting and Trading, -, University of Leiden, Netherland.
Chiarella, C. & Ziogas, A. 2004, 'Pricing American options on jump-diffusion processes using Fourier-Hermite series expansions', -, Computing in Economics and Finance 2004, -, Arsterdam, Netherlands.
Chiarella, C. & Ziogas, A. 2004, 'Pricing American options on jump-diffusion processes: Analytical results and numerical methods', -, Quantitative Methods in Finance Conference 2004, -, Sydney, Australia.
Asada, T., Chen, P., Chiarella, C. & Flaschel, P. 2004, 'Keynesian Dynamics and the Wage Price Spiral. A Baseline Disequilibrium Approach'.
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We reformulate and extend the standard AS-AD growth model of the
Neoclassical Synthesis (Stage I) with its traditional microfoundations.
The model still has an LM curve in the place of a Taylor interest rate
rule, exhibits sticky wages as well as sticky prices, myopic perfect
foresight of current inﬂation rates and adaptively formed medium
run expectations concerning the investment and inﬂation climate
in which the economy is operating. The resulting nonlinear 5D model of
labor and goods market disequilibrium dynamics avoids striking anomalies
of the standard model of the Neoclassical synthesis (Stage I). It
exhibits instead Keynesian feedback dynamics proper with in particular
asymptotic stability of its unique interior steady state for low
adjustment speeds and with cyclical loss of stability ? by way of Hopf
bifurcations ? when some adjustment speeds are made suficiently large,
even leading to purely explosive dynamics sooner or later. In such cases
downward money wage rigidity can be used to make the dynamics bounded
and thus viable. In this way we obtain and analyze a baseline DAS-AD
model with Keynesian feedback channels whose rich set of stability
features is the source of business cycle ﬂuctuations. These
outcomes of the model stand in contrast to those of the currently
fashionable New Keynesian alternative (the Neoclassical Synthesis, Stage
II) that we suggest is more limited in scope.
Chiarella, C. & He, X.Z. 2003, 'Heterogeneous beliefs, risk, and learning in a simple asset-pricing model with a market maker', MACROECONOMIC DYNAMICS, pp. 503-536.
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Chiarella, C. & Tô, T.-.D. 2003, 'The Jump Component of the Volatility Structure of Interest Rate Futures Markets: An International Comparison', Journal of Futures Markets, pp. 1125-1158.
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We propose a generalization of the Shirakawa (1991) model to capture the jump component in fixed-income markets. The model is formulated under the Heath, Jarrow, & Morton (1992) framework, and allows the presence of a Wiener noise and a finite number of Poisson noises, each associated with a time deterministic volatility function. We derive the evolution of the futures price and use this evolution to estimate the model parameters via the likelihood transformation technique of Duan (1994). We apply the method to the short-term futures contracts traded on CME, SFE, LIFFE, and TIFFE, and find that each market is characterized by very different behavior. © 2003 Wiley Periodicals, Inc.
Chiarella, C. & Kwon, O.K. 2003, 'Finite dimensional affine realisations of HJM models in terms of forward rates and yields', Review of Derivatives Research, pp. 129-155.
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Finite dimensional Markovian HJM term structure models provide ideal settings for the study of term structure dynamics and interest rate derivatives where the flexibility of the HJM framework and the tractability of Markovian models coexist. Consequently, these models became the focus of a series of papers including Carverhill (1994), Ritchken and Sankarasubramanian (1995), Bhar and Chiarella (1997), Inui and Kijima (1998), de Jong and Santa-Clara (1999), Björk and Svensson (2001) and Chiarella and Kwon (2001a). However, these models usually required the introduction of a large number of state variables which, at first sight, did not appear to have clear links to the market observed quantities, and the explicit realisations of the forward rate curve in terms of the state variables were unclear. In this paper, it is shown that the forward rate curves for these models are affine functions of the state variables, and conversely that the state variables in these models can be expressed as affine functions of a finite number of forward rates or yields. This property is useful, for example, in the estimation of model parameters. The paper also provides explicit formulae for the bond prices in terms of the state variables that generalise the formulae given in Inui and Kijima (1998), and applies the framework to obtain affine representations for a number of popular interest rate models.
Chiarella, C. & He, X. 2003, 'Asset pricing and wealth dynamics - an adaptive model with heterogenous agents', WEHIA 2003, 8th Annual Workshop on Economics with Heterogeneous Interacting Agents, Institute of Economics, Keil, Germany, pp. 1-20.
Bhar, R., Chiarella, C. & To, T. 2003, 'Estimating the volatility structure of Eurodollar futures contracts within a Heath-Jarrow-Morton framework', 20th AFFI International Conference 2003, AFFI International Conference 2003, The Association Francaise de Finance, Lyon, France, pp. 1-42.
Chiarella, C. 2003, 'McKean's method applied to American call options on jump-diffusion processes', 2nd National Symposium on Financial Mathematics, --, Sydney, Australia.
Chiarella, C. 2003, 'McKean's method applied to American call options on jump-diffusion processes', Quantitative Methods in Finance 2003 Conference, --, Sydney, Australia.
Chiarella, C. & To, T. 2003, 'The jump component of the volatility structure of interest rate futures markets: An international comparison', 13th Asia-Pacific Futures Research Symposium, 13th Asia-Pacific Futures Research Symposium, --, Shanghai, China.
Chiarella, C., Flaschel, P., He, X. & Hung, H. 2003, 'A stochastic model of real-financial interaction with boundedly rational heterogeneous agents', Bielefeld Workshop on Real-Financial Interaction, --, Bielefeld, Germany.
Chiarella, C. & He, X. 2003, 'An adaptive model of asset pricing and wealth dynamics with heterogeneous trading strategies', WEHIA 2003 - Annual Workshop on Economics with Heterogeneous Interacting Agents, --, Keil, Germany.
Chiarella, C., He, X. & Zhu, P. 2003, 'Fading memory learning in the cobweb model with risk averse heterogeneous producers', 9th International Conference on Computing in Economics and Finance, --, Seattle, USA.
Chiarella, C. & Nikitopoulos Sklibosios, C. 2003, 'A jump-diffusion bond pricing model within the HJM frame work', Japanese Association Financial Econometrics and Engineering Meeting, --, Tokyo, Japan.
Chiarella, C. & Nikitopoulos Sklibosios, C. 2003, 'An implementation of the Shirakawa jump-diffusion term structure model', 9th International Conference on Computing in Economics and Finance, --, Seattle, USA.
Chiarella, C. & Ziogas, A. 2003, 'McKean's method applied to American call options on jump-diffusion processes', 9th International Conference on Computing in Economics and Finance, --, Seattle, USA.
Fouque, J.-.P. & Han, C.-.H. 2003, 'Pricing Asian options with stochastic volatility', Quantitative Finance, pp. 353-362.
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In this paper, we generalize the recently developed dimension reduction technique of Vecer for pricing arithmetic average Asian options. The assumption of constant volatility in Vecer's method will be relaxed to the case that volatility is randomly fluctuating and is driven by a mean-reverting (or ergodic) process. We then use the fast mean-reverting stochastic volatility asymptotic analysis introduced by Fouque, Papanicolaou and Sircar to derive an approximation to the option price which takes into account the skew of the implied volatility surface. This approximation is obtained by solving a pair of one-dimensional partial differential equations.
Bhar, R., Chiarella, C. & To, T.D. 2002, 'A Maximum Likelihood Approach to Estimation of Heath-Jarrow-Morton Models'.
Research on the Heath-Jarrow-Morton (1992) term structure models so far has focused on the class having time-deterministic instantaneous forward rate volatility. In this case the forward rate is
Markovian, even if the spot rate process is not. However, this Markovian feature can only be used under the historical measure, involving two unsatisfactory assumptions: one on market price risk, usually
made for pure mathematical tractability, the other to use futures yields as a proxy for the instantaneous forward rate, which may result in estimation bias. This paper circumvents both of these assumptions.
First, the bias is quantified and shown to be non-negligible. Then futures contracts are treated as derivative instruments written on forward rates to derive the full information maximum likelihood
estimator for observable futures prices, using both time series and cross-sectional data, without the need to assume and estimate any functional forms for the market price of interest rate risk. The
derivation involves the likelihood transformation method of Duan (1994). The method is then applied to the estimation of a humped forward rate volatility model for Eurodollar futures series traded on the
Chicago Mercantile Exchange.
Bischi, G., Chiarella, C. & Kopel, M.O. 2002, 'On market games with misspecified demand functions long run outcomes and global dynamics', Society for Computational Economics Conference, Society for Computational Economics Conference, Aix-En-Provence, France.
Chiarella, C. 2002, 'A maximum likelihood approach to estimation of Heath-Jarrow-Morton models', Econometic Society Australasian Meeting, Econometric Society Australasian Meeting, Brisbane, Australia.
Nikitopoulos Sklibosios, C. & Chiarella, C. 2002, 'A jump diffusion derivative pricing model arising within the Heath-Jarrow-Morton framework', 2nd World Congress of the Bachelier Finance Society, 2nd World Congress of the Bachelier Finance Society, Knossos,Crete.
Chiarella, C. 2002, 'On estimation of interest rate volatility structure within the HJM framework', Quantitative Methods on Finance 2002 Conference, Quantitative Methods on Finance 2002 Conference, Sydney and Cairns, australia.
Chiarella, C. 2002, 'Real-financial interaction: A stochastic Blanchard model with a state-of-market reaction co-efficient', Workshop on Macrodynamics, Real-Financial Interaction and the Labor Market, Workshop on Macrodynamics, Real-Financial Interaction and the Labor Market, Bielefeld, Germany.
Chiarella, C., Bhar, R. & Runggaldier, W.J. 2002, 'Estimation of interest rate models by use of a bayesian algorithm', 8th International Conference on Forecasting Financial Markets, 8th International Conference on Forecasting Financial Markets, London, UK.
Chiarella, C., Bhar, R., Runggaldier, W.J. & Zhu, P. 2002, 'The volatility of the spot interest rate implied by arbitrage', Forecasting Financial Markets Conference, Forecasting Financial Markets Conference, London, UK.
Chiarella, C., Craddock, M.J. & El-Hassan, N. 2002, 'A short time expansion of the volatility function for the calibration of option pricing models', Society of Computational Economics Conference, Society of Computational Economics Conference, Aix-en-Provence, France.
Chiarella, C., Dieci, R. & Gardini, L. 2002, 'Price dynamics and diversification under heterogeneous expectations', Society for Computational Economics Conference, Society for Computational Economics Conference, Aix-En-Provence, France.
Chiarella, C., Flaschel, P., Gong, G. & Semmler, W. 2002, 'Nonlinear Phillips curves, the emergence of complex dynamics and the role of monetary policy role', Society for Computational Economics Conference, Society for Computational Economics Conference, Aix en Provence, France.
Chiarella, C., Gallegati, M., Leombruni, R. & Palestrini, A. 2002, 'Asset price dynamics among heterogenous interacting agents', Society for Computational Economics Agents, Society for Computational Economics Conference, Aix en Province, France.
Chiarella, C. & He, X. 2002, 'Adaptive models of asset pricing and wealth dynamics in economies with heterogeneous agents', Workshop on Economic Dynamics - CENDEF, Workshop on Economic Dynamics - CENDEF, University of Leiden, The Netherlands.
Chiarella, C. & He, X.-.Z. 2002, 'An Adaptive Model on Asset Pricing and Wealth Dynamics with Heterogeneous Trading Strategies'.
This paper develops an adaptive model on asset pricing and wealth dynamic of a financial market with heterogeneous agents and examines the profitability of momentum and contrarian trading
strategies. In order to characterize asset price, wealth dynamics and rational adaptiveness arising from the interaction of heterogeneous agents with CRRA utility, an adaptive discrete time equilibrium
model in terms of return ad wealth proportions (among heterogeneous representative agents) is established. Taking trend followers and contrarians as the main hetergeneous agents in the model, the
profitability of momentum and contrarian trading strategies is analyzed. Our results show the capability of the model to characterize some of the existing evidence on many of anomailies observed in
financial markets, including the profitability of momentum trading strategies over short time intervals, rational adaptiveness of agents, overconfidence and underreaction, overreaction and herd behavior,
excess volatility, and volatility clustering.
Chiarella, C. & He, X. 2002, 'An adaptive model on asset pricing and wealth dynamics with heterogeneous trading systems', Asia Pacific Finance Association Conference, Asia Pacific Finance Association Conference, Tokyo, Japan.
Chiarella, C. & Iori, G. 2002, 'A simple microstructure model of double auction markets', Society for Computational Economics, Society for Computational Economics Conference, Aix en Province, France.
Chiarella, C. & Kwon, O. 2002, 'Finite dimensional realisations of HJM models in terms of forward rates and yields', Asia Pacific Finance Association Conference, Asia Pacific Finance Association Conference, Tokyo, Japan.
Chiarella, C. & Musti, S. 2002, 'Numerical investigations of the HJM model with forward rate dependent volatility', Society for Computational Economics Conference, Society for Computational Economics Conference, Aix En Provence, France.
Chiarella, C. & Ziogas, A. 2002, 'Evaluation of American strangles', Society for Computational Economics Conference, Society for Computational Economics Conference, Aix en Province, France.
Chiarella, C., Semmler, W., Mittnik, S. & Zhu, P.Y. 2002, 'Stock market, interest rate and output: A model and estimation for US time series data', STUDIES IN NONLINEAR DYNAMICS AND ECONOMETRICS.
Engel, A., Chiarella, C., Szidarovszky, F., IEEE, IEEE, IEEE & IEEE 2002, 'A game theoretical model of international fishing with time delay', 2001 IEEE INTERNATIONAL CONFERENCE ON SYSTEMS, MAN, AND CYBERNETICS, VOLS 1-5, pp. 2658-2663.
Chiarella, C. & El-Hassan, N. 2001, 'Evaluating barrier options using Fourier-Hermite expansions', 8th Annual Asia-Pacific Finance Association Conference, Bangkok, Thailand.
Chiarella, C. & El-Hassan, N. 2000, 'The evaluation of point barrier options in a path integral framework', 4th Columbia-JAFFEE Conference Proceedings, Columbia-JAFFEE Conference, JAFFEE, Tokyo, Japan, pp. 103-126.
Chiarella, C., El-Hassan, N. & Kucera, A. 2000, 'The evaluation of multiasset European and American options via Fourier-Hermite series expansions', Sixth International Conference on Computing in Economics and Finance, Barcelona, Spain.
Chiarella, C., El-Hassan, N. & Kucera, A. 2000, 'The evaluation of point barrier options in a path integral framework', Seventh International Conference on Computational Finance/Forecasting Financial Markets, London, UK.
Chiarella, C., El-Hassan, N. & Kucera, A. 1997, 'Evaluation of derivative security prices in a path integral framework using Fourier-Hermite series expansions', JIC97, Japanese Association of Financial Econometrics and Engineering, Tokyo, Japan, pp. 350-372.
Bhar, R. & Chiarella, C. 1997, 'The estimation of the Heath-Jarrow-Morton model by use of Kalman filtering techniques', COMPUTATIONAL APPROACHES TO ECONOMIC PROBLEMS, pp. 113-126.
Bhar, R., Chiarella, C. & IEEE 1996, 'Interest rate futures: Estimation of volatility parameters in an arbitrage-free framework', PROCEEDINGS OF THE IEEE/IAFE 1996 CONFERENCE ON COMPUTATIONAL INTELLIGENCE FOR FINANCIAL ENGINEERING (CIFER), pp. 168-182.
CHIARELLA, C., PHAM, T., SIM, A. & TAN, M. 1992, 'DETERMINANTS OF CORPORATE CAPITAL STRUCTURE - AUSTRALIAN EVIDENCE', PACIFIC-BASIN CAPITAL MARKETS RESEARCH VOLUME III, pp. 139-158.
Ziogas, A., Cheang, G. & Chiarella, C., 'The Valuation of Multiple Asset American Options under Jump Diffusion Processes'.
We consider American versions of multiple asset options when the underlying assets follow jump-diffusion processes, for example exchange options and max-options. We consider various representations of the option value and in particular apply Fourier transform techniques to the integro-partial differential equations determining the option value to obtain the jump-diffusion extension of Kim's integral equation. We also discuss the corresponding perpetual option and the shape of the early exercise region. We particularly focus on numerical implementations when the jump times are governed by a Poisson process and the jump sizes are lognormally distributed. We compare the efficacy of the method of lines, the Crank-Nicholson scheme and solution of the integral equations in generating numerical values of the option
Economics, F.U.O.T.S.G.M.S.O.M.G.I.O.T.A.Z.S.O., Cheang, G.H.L., Chiarella, C., Meyer, G. & Ziogas, A., 'Numerical Methods for American Spread Options under Jump Diffusion Processes'.
This paper examines two numerical methods for pricing of American
spread options in the case where both underlying assets follow the
jump-diffusion process of Merton (1976). We extend the integral
equation representation for the American spread option presented by
Broadie and Detemple (1997) to the case where the return dynamics for
both underlying assets involve jump terms. By use of the Fourier
transform method, we derive a linked system of integral equations for
the price and early exercise boundary of the American spread
option. We also provide an integral equation for the delta of the
American spread option, and determine the limit of the early exercise
surface as time to expiry tends to zero. We consider two numerical
methods for computing the price, delta and early exercise boundary of
the American spread option. The first method is a two-dimensional
generalisation of the method of lines for jump-diffusion, extending on
the algorithm of Meyer (1998). The second method involves a numerical
integration scheme for Volterra integral equations. This algorithm
extends the methods of Kallast and Kivinukk (2003) and Chiarella and
Ziogas (2004) to the two-dimensional jump-diffusion setting. The
methods are benchmarked against a suitable Crank-Nicolson finite
difference scheme, and their efficiency is explored.
Chiarella, C. & Ziogas, A., 'Pricing American Options under Stochastic Volatility and Jump Diffusion Dynamics'.
This paper considers the problem of pricing American options when the
dynamics of the underlying are driven both by stochastic volatility following a square
root process as used by Heston (1993) and by a Poisson jump process as introduced
by Merton (1976). The two-factor homogeneous integro-partial differential equation
for the price and early exercise surface is cast into an in-homogeneous form accord-
ing to the approach introduced by Jamshidian (1992). The Fourier transform is then
applied to find the solution, which generalizes in an obvious way the structure of the
solution to the corresponding European option pricing problem in the case of a call
option and constant interest rates obtained by Scott (1997). The price is given by an
integral equation dependent upon the early exercise surface, for which a correspond-
ing integral equation is obtained. An algorithm is proposed for solving the integral
equation system. The method is implemented, and the resulting prices and deltas are
compared with the constant volatility model. The computational efficiency of the nu-
merical integration scheme is also considered by comparing with benchmark solutions
obtained by a finite difference method and the method of lines applied directly to the
integro-partial differential equation
We reconsider the derivation of the traditional capital asset pricing
model (CAPM) in the discrete time setting for a portfolio of one
riskless asset and many risky assets. In contrast to the standard
setting, it is assumed that agents are heterogeneous in their
conditional means and covariances of the risky returns, and that their
beliefs about future returns - based on statistical properties of past
returns - induce expectations feedback. A Walrasian auctioneer
scenario is used for the determination of the market clearing
price. In this framework we first construct a consensus belief to
represent the aggregate market beliefs about means and
variances/covariances of returns, and derive a heterogeneous CAPM
which relates aggregate excess return on risky assets with aggregate
excess return on the market portfolio via aggregate beta
coefficients. We then use this result to establish a dynamic {\em
market fraction\/} model in which agents are grouped according to
their beliefs. In particular, we focus on three classical
heterogeneous agents types - fundamentalists, trend followers and
noise traders - and investigate how some of the key agent
characteristics affect the time varying behaviour of market returns
and beta coefficients
Chiarella, C., Dieci, R. & He, T., 'Aggregation of Heterogeneous Beliefs and Asset Pricing: A Mean-Variance Analysis'.
The aim of this paper is to show, within the mean-variance framework,
how the market belief can be constructed as the result of the
aggregation of heterogeneous beliefs and how the market equilibrium
prices of risky assets can thus be determined. The heterogeneous
beliefs are defined in terms of not only the means but also variances
and covariances. By constructing the mean and variance of the market
belief, we analyze the impact of the heterogeneous beliefs on the
market equilibrium asset pricing relation. In particular, we extend
the standard CAPM under homogenous beliefs to the one under the
heterogeneous beliefs.
Journal articles
Chiarella, C. & Di Guilmi, C. 2015, 'The limit distribution of evolving strategies in financial markets', Studies in Nonlinear Dynamics and Econometrics, vol. 19, no. 2, pp. 137-159.
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This paper reconsiders the popular Brock and Hommes [Brock, W. A., and C. H. Hommes. 1997. 'A Rational Route to Randomness.' Econometrica 65: 1059-1096.] framework for the study of the evolution of agents' choices when different behavioural strategies are available. In particular, we model the intensity of choice as an endogenous variable and not a parameter as it is commonly treated in the literature. We make use of the maximum entropy inference to obtain an analogous exponential type probability function for strategies, with the intensity of choice varying over time according to the performance of each strategy. We test this approach on an existing asset pricing model, highlighting the effects on the system of the different switching pattern that originate in the endogenous switching intensity.
Caldana, R., Cheang, G.H.L., Chiarella, C. & Fusai, G. 2015, 'Correction: Exchange Option under Jump-diffusion Dynamics', Applied Mathematical Finance, vol. 22, no. 1, pp. 99-103.
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MINA, K.A.R.L.F.R.I.E.D.R.I.C.H., CHEANG, G.E.R.A.L.D.H.L. & CHIARELLA, C.A.R.L. 2015, 'APPROXIMATE HEDGING OF OPTIONS UNDER JUMP-DIFFUSION PROCESSES', International Journal of Theoretical and Applied Finance, pp. 1550024-1550024.
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Chiarella, C. & Ziveyi, J. 2014, 'Pricing American options written on two underlying assets', QUANTITATIVE FINANCE, vol. 14, no. 3, pp. 409-426.
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Chiarella, C. & Di Guilmi, C. 2014, 'Financial instability and debt deflation dynamics in a bottom-up approach', Economics Bulletin, vol. 34, no. 1, pp. 125-132.
In this paper we expand the agent based model introduced by Chiarella and Di Guilmi (Chiarella, C. and Di Guilmi, C., The financial instability hypothesis: A stochastic microfoundation framework. Journal of Economic Dynamics and Control, 35(8):1151 – 1171, 2011) in which the business cycle originates by the modifications in firms' balance sheets induced by their investment decisions. During periods of market euphoria, firms increase their capital stock and their level of debt. At the same time the increasing availability of liquidity
for investors causes inflation in asset price. When firms' debt reaches an unsustainable level the virtuous cycle is reversed in a depression. We modify the original model in order to study the impact of the dependence of firms' expectations on the stock market performance and of the rise in the proportion of Ponzi firms. We also run a further computational experiment to assess the effect of the buy-back of firms' shares.
Chiarella, C., Griebsch, S. & Kang, B. 2014, 'A comparative study on time-efficient methods to price compound options in the Heston model', Computers and Mathematics with Applications, vol. 67, no. 6, pp. 1254-1270.
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The primary purpose of this paper is to provide an in-depth analysis of a number of structurally different methods to numerically evaluate European compound option prices under Heston's stochastic volatility dynamics. Therefore, we first outline several approaches that can be used to price these type of options in the Heston model: a modified sparse grid method, a fractional fast Fourier transform technique, a (semi-)analytical valuation formula using Green's function of logarithmic spot and volatility and a Monte Carlo simulation. Then we compare the methods on a theoretical basis and report on their numerical properties with respect to computational times and accuracy. One key element of our analysis is that the analyzed methods are extended to incorporate piecewise time-dependent model parameters, which allows for a more realistic compound option pricing. The results in the numerical analysis section are important for practitioners in the financial industry to identify under which model prerequisites (for instance, Heston model where Feller condition is fulfilled or not, Heston model with piecewise time-dependent parameters or with stochastic interest rates) it is preferable to use and which of the available numerical methods. © 2014 Elsevier Ltd. All rights reserved.
Chiarella, C., He, X.-.Z. & Zwinkels, R.C.J. 2014, 'Heterogeneous expectations in asset pricing: Empirical evidence from the S & P500', JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION, vol. 105, pp. 1-16.
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Lian, G., Chiarella, C. & Kalev, P. 2014, 'Volatility swaps and volatility options on discretely sampled realized variance', Journal of Economic Dynamics and Control, vol. 47, pp. 239-262.
Kontoghiorghes, E.J., Van Dijk, H.K., Belsley, D.A., Bollerslev, T., Diebold, F.X., Dufour, J.-.M., Engle, R., Harvey, A., Koopman, S.J., Pesaran, H., Phillips, P.C.B., Smith, R.J., West, M., Yao, Q., Amendola, A., Billio, M., Chen, C.W.S., Chiarella, C., Colubi, A., Deistler, M., Francq, C., Hallin, M., Jacquier, E., Judd, K., Koop, G., Luetkepohl, H., MacKinnon, J.G., Mittnik, S., Omori, Y., Pollock, D.S.G., Proietti, T., Rombouts, J.V.K., Scaillet, O., Semmler, W., So, M.K.P., Steel, M., Taylor, R., Tzavalis, E., Zakoian, J.-.M., Boswijk, H.P., Luati, A., Maheu, J. & Board, C.A. 2014, 'CFEnetwork: The Annals of Computational and Financial Econometrics 2nd Issue', COMPUTATIONAL STATISTICS & DATA ANALYSIS, vol. 76, pp. 1-3.
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Chiarella, C., Da Fonseca, J. & Grasselli, M. 2014, 'Pricing range notes within Wishart affine models', Insurance: Mathematics and Economics, vol. 58, pp. 193-203.
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This paper proposes a model for credit default swap (CDS) spreads under heterogeneous expectations to explain the escalation in sovereign European CDS spreads and the widening variations across European sovereigns following the Global Financial Crisis (GFC). In our model, investors believe that sovereign CDS spreads are determined by country-specific fundamentals and momentum. By estimating the model we find evidence that, while some of the recent movements in sovereign CDS spreads can be explained by deteriorating fundamentals for core European Union (EU) countries, momentum has also played a destabilizing role since the GFC in all sovereign credit markets studied.
Cheang, G.H., Chiarella, C. & Ziogas, A. 2013, 'The representation of American options prices under stochastic volatility and jump-diffusion dynamics', Quantitative Finance, vol. 13, no. 2, pp. 241-253.
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This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square-root process as used by Heston [Rev. Financial Stud., 1993, 6, 327½343], and by a Poisson jump process as introduced by Merton [J. Financial Econ., 1976, 3, 125½144]. Probability arguments are invoked to find a representation of the solution in terms of expectations over the joint distribution of the underlying process. A combination of Fourier transform in the log stock price and Laplace transform in the volatility is then applied to find the transition probability density function of the underlying process. It turns out that the price is given by an integral dependent upon the early exercise surface, for which a corresponding integral equation is obtained. The solution generalizes in an intuitive way the structure of the solution to the corresponding European option pricing problem obtained by Scott [Math. Finance, 1997, 7(4), 413½426], but here in the case of a call option and constant interest rates
Matsumoto, A., Chiarella, C. & Szidarovszky, F. 2013, 'Dynamic monopoly with bounded continuously distributed delay', CHAOS SOLITONS & FRACTALS, vol. 47, pp. 66-72.
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This article presents a continuous-time model of exchange rates not only relying on macroeconomic factors but also having an investor heterogeneity component. The driving macroeconomic factor is the domestic½foreign interest rate differential, while the investor heterogeneity is described by the expectations of boundedly rational portfolio managers who use a weighted average of the expectations of fundamentalists and chartists. Within this framework, the different roles of the macroeconomic factor and investor heterogeneity in the determination of the exchange rate are examined explicitly. We show that this simple model generates very complicated market behaviour, including the existence of multiple steady-state equilibria, deviations of the market exchange rate from the fundamental one and market fluctuations. Numerical simulation of the corresponding stochastic version of the model shows that the model is able to generate typical time series and volatility clustering patterns observed in exchange rate markets.
The conditional CAPM with time-varying betas has been widely used to explain the cross-section of asset returns. However, most of the literature on time-varying beta is motivated by econometric estimation using various latent risk factors rather than explicit modelling of the stochastic behaviour of betas through agents behaviour, such as momentum trading. Misspecification of beta risk and the lack of any theoretical guidance on how to specify risk factors based on the representative agent economy appear empirically challenging. In this paper, we set up a dynamic equilibrium model of a financial market with boundedly rational and heterogeneous agents within the mean-variance framework of repeated one-period optimisation and develop an explicit dynamic behaviour CAPM relation between the expected equilibrium returns and time-varying betas. By incorporating the two most commonly used types of investors, fundamentalists and chartists, into the model, we show that there is a systematic change in the market portfolio, risk-return relationships, and time varying betas when investors change their behaviour, such as the chartists acting as momentum traders. In particular, we demonstrate the stochastic nature of time-varying betas. We also show that the commonly used rolling window estimates of time-varying betas may not be consistent with the ex-ante betas implied by the equilibrium model. The results provide a number of insights into an understanding of time-varying beta.
Chiarella, C., Dieci, R., He, X.-.Z. & Li, K. 2013, 'An evolutionary CAPM under heterogeneous beliefs', Annals of Finance, vol. 9, no. 2, pp. 185-215.
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Heterogeneity and evolutionary behaviour of investors are two of the most important characteristics of financial markets. This paper incorporates the adaptive behaviour of agents with heterogeneous beliefs and establishes an evolutionary capital asset pricing model (ECAPM) within the mean-variance framework. We show that the rational behaviour of agents switching to better-performing trading strategies can cause large deviations of the market price from the fundamental value of one asset to spill over to other assets. Also, this spill-over effect is associated with high trading volumes and persistent volatility characterized by significantly decaying autocorrelations of, and positive correlation between, price volatility and trading volume. © 2012 Springer-Verlag Berlin Heidelberg.
Chiarella, C., Matsumoto, A. & Szidarovszky, F. 2013, 'Isoelastic oligopolies under uncertainty', APPLIED MATHEMATICS AND COMPUTATION, vol. 219, no. 21, pp. 10475-10486.
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Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T.D. 2013, 'Humps in the volatility structure of the crude oil futures market: New evidence', Energy Economics, vol. 40, no. 1, pp. 989-1000.
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This paper analyses the volatility structure of commodity derivatives markets. The model encompasses hump-shaped, unspanned stochastic volatility, which entails a finite-dimensional affine model for the commodity futures curve and quasi-analytical prices for options on commodity futures. Using an extensive database of crude oil futures and futures options spanning 21 years, we find the presence of hump-shaped, partially spanned stochastic volatility in the crude oil market. The hump shaped feature is more pronounced when the market is more volatile, and delivers better pricing as well as hedging performance under various dynamic factor hedging schemes.
Chiarella, C. & Ziveyi, J. 2013, 'American option pricing under two stochastic volatility processes', Applied mathemetics and computation, vol. 224, no. 1, pp. 283-310.
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In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes as proposed in Christoffersen, Heston and Jacobs (2009) [13]. We consider the associated partial differential equation (PDE) for the option price and its solution. An integral expression for the general solution of the PDE is presented by using Duhamels principle and this is expressed in terms of the joint transition density function for the driving stochastic processes. For the particular form of the underlying dynamics we are able to solve the Kolmogorov PDE for the joint transition density function by first transforming it to a corresponding system of characteristic PDEs using a combination of Fourier and Laplace transforms. The characteristic PDE system is solved by using the method of characteristics. With the full price representation in place, numerical results are presented by first approximating the early exercise surface with a bivariate log linear function. We perform numerical comparisons with results generated by the method of lines algorithm and note that our approach provides quite good accuracy
Chiarella, C. & Kang, B. 2013, 'The evaluation of American compound option prices under stochastic volatility and stochastic interest rates', Journal of Computational Finance, vol. 17, no. 1, pp. 71-92.
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A compound option (the mother option) gives the holder the right, but not the obligation, to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we consider the problem of pricing American-type compound options when the underlying dynamics follow Heston 's stochastic volatility and with stochastic interest rate driven by Cox-Ingersoll-Ross processes. We use a partial differential equation (PDE) approach to obtain a numerical solution. The problem is formulated as the solution to a two-pass free-boundary PDE problem, which is solved via a sparse grid approach and is found to be accurate and efficient compared with the results from a benchmark solution based on a least-squares Monte Carlo simulation combined with the projected successive over-relaxation method.
Chiarella, C. 2013, 'Le prospettive per la teoria economica nei prossimi 30 anni', Pristem Storis: note di matematica, storia e cultura, vol. 31, no. Feb, pp. 79-88.
Questo articolo riassume gli sviluppi nella teoria economica durante gli ultimi settanta anni. Si evidenzia come la teoria abbia oscillato fra due punti di vista, quello keynesiano negli anni '30, per poi successivamente essere dominata dal punto di vista neoclassico. Recentemente Ie idee keynesiane sono state oggetto di un rinnovato interesse. I;articolo esamina anche i principali metodi matematici dei due campi.
CHIARELLA, C.A.R.L., MAINA, S.A.M.U.E.L.C.H.E.G.E. & SKLIBOSIOS, C.H.R.I.S.T.I.N.A.N.I.K.I.T.O.P.O.U.L.O.S. 2013, 'CREDIT DERIVATIVES PRICING WITH STOCHASTIC VOLATILITY MODELS', International Journal of Theoretical and Applied Finance, vol. 16, no. 04.
This paper proposes a model for pricing credit derivatives in a defaultable HJM framework. The model features hump-shaped, level dependent, and unspanned stochastic volatility, and accommodates a correlation structure between the stochastic volatility, the default-free interest rates, and the credit spreads. The model is finite-dimensional, and leads (a) to exponentially affine default-free and defaultable bond prices, and (b) to an approximation for pricing credit default swaps and swaptions in terms of defaultable bond prices with varying maturities. A numerical study demonstrates that the model captures stylized various features of credit default swaps and swaptions.
Financial markets are typically characterized by high (low) price level and low (high) volatility during boom (bust) periods, suggesting that price and volatility tend to move together with different market conditions/states. By proposing a simple heterogeneous agent model of fundamentalists and chartists with Markov chain regime-dependent expectations and applying the S&P 500 data from January 2000 to June 2010, we show that the estimation of the model matches well with the boom and bust periods in the US stock market. In addition, we find evidence of time-varying behavioural heterogeneity within-group and that the model exhibits good forecasting accuracy. © 2012 Elsevier B.V. All rights reserved.
Chiarella, C., He, X. & Pellizzari, P. 2012, 'A dynamic analysis of the microstructure of moving average rules in a double auction market', Macroeconomic Dynamics, vol. 16, no. 4, pp. 556-575.
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Inspired by the theoretically oriented dynamic analysis of moving average rules in the model of Chiarella, He, and Hommes (CHH) [Journal of Economic Dynamics and Control 30 (2006), 1729-1753], this paper conducts a dynamic analysis of a more realistic microstructure model of continuous double auctions in which the probability of heterogeneous agents trading is determined by the rules of either fundamentalists mean-reverting to the fundamental or chartists choosing moving average rules based on their relative performance. With such a realistic market microstructure, the model is able not only to obtain the results of the CHH model but also to characterize most of the stylized facts including volatility clustering, insignificant autocorrelations (ACs) of returns, and significant slowly decaying ACs of the absolute returns. The results seem to suggest that a comprehensive explanation of several statistical properties of returns is possible in a framework where both behavioral traits and realistic microstructure have a role
Chiarella, C., Flaschel, P., Koeper, C., Proano, C. & Semmler, W. 2012, 'Macroeconomic Stabilization Policies in Intrinsically Unstable Macroeconomies', STUDIES IN NONLINEAR DYNAMICS AND ECONOMETRICS, vol. 16, no. 2.
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Chiarella, C., Kang, B. & Meyer, G. 2012, 'The evaluation of barrier option prices under stochastic volatility', Computers & Mathematics With Applications, vol. 64, no. 6, pp. 2034-2048.
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This paper considers the problem of numerically evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Heston (1993)[7]. We develop a method of lines approach to evaluate the price as well as the delta and gamma of the option. The method is able to efficiently handle both continuously monitored and discretely monitored barrier options and can also handle barrier options with early exercise features. In the latter case, we can calculate the early exercise boundary of an American barrier option in both the continuously and discretely monitored cases.
Giansante, S., Chiarella, C., Sordi, S. & Vercelli, A. 2012, 'Structural contagion and vulnerability to unexpected liquidity shortfalls', JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION, vol. 83, no. 3, pp. 558-569.
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Chiarella, C., Flaschel, P., Hartmann, F. & Proaño, C.R. 2012, 'Stock market booms, endogenous credit creation and the implications of broad and narrow banking for macroeconomic stability', Journal of Economic Behavior and Organization.
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In this paper we study the implications of the present broad banking system for macroeconomic stability. We show that when commercial banks are allowed to trade in financial assets (here equities) as a substitute for traditional lending, the macroeconomic system is likely to be an unstable one. We then consider a narrow banking system defined by a Fisherian 100 percent reserve ratio for checkable deposits and the ban for commercial banks from trading in stocks and other financial assets. Within the stylized theoretical framework set up here, we show that in the second system macroeconomic stability is guaranteed by some weak assumptions on the behavior of economic agents. Moreover, while a sufficient loan supply can be guaranteed in such a framework, the rationale for bank runs can be eliminated, in contrast to what is likely to happen under traditional broad banking. Though narrow banking is an extreme banking system unlikely to be adopted in the short-run, its features highlight the stability and efficiency properties that the separation between commercial and investment banking bring about. © 2012 Elsevier B.V. All rights reserved.
This paperexaminesthedynamicsoffinancialdistressandinparticularthemechanism of transmissionofshocksfromthefinancialsectortotherealeconomy.Theanalysisis performedbyrepresentingthelinkagesbetweenmicroeconomicfinancialvariablesand the aggregateperformanceoftheeconomybymeansofamicrofoundedmodelwith firms thathaveheterogeneouscapitalstructures.Themodelissolvedbothnumerically and analytically,bymeansofastochasticapproximationthatisabletoreplicatequite well thenumericalsolution.Thesemethodologies,byovercomingtherestrictions imposedbythetraditionalmicrofoundedapproach,enableustoprovidesomeinsights into thestabilizationpolicieswhichmaybeeffectiveinafinanciallyfragilesystem.
Chiarella, C., He, X.-.Z. & Zheng, M. 2011, 'An analysis of the effect of noise in a heterogeneous agent financial market model', Journal of Economic Dynamics and Control, vol. 35, no. 1, pp. 148-162.
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Heterogeneous agent models (HAMs) in finance and economics are often characterised by high dimensional nonlinear stochastic differential or difference systems. Because of the complexity of the interaction between the nonlinearities and noise, a commonly used, often called indirect, approach to the study of HAMs combines theoretical analysis of the underlying deterministic skeleton with numerical analysis of the stochastic model. However, it is well known that this indirect approach may not properly characterise the nature of the stochastic model. This paper aims to tackle this issue by developing a direct and analytical approach to the analysis of a stochastic model of speculative price dynamics involving two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the stationary measures of a stochastic dynamical system. Using the stochastic method of averaging and stochastic bifurcation theory, we show that the stochastic model displays behaviour consistent with that of the underlying deterministic model when the time lag in the formation of price trends used by the chartists is far away from zero. However, when this lag approaches zero, such consistency breaks down. © 2010 Elsevier B.V.
Asada, T., Chiarella, C., Flaschel, P., Mouakil, T., Proano, C. & Semmler, W. 2011, 'STOCK-FLOW INTERACTIONS, DISEQUILIBRIUM MACROECONOMICS AND THE ROLE OF ECONOMIC POLICY', JOURNAL OF ECONOMIC SURVEYS, vol. 25, no. 3, pp. 569-599.
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Bischi, G.I., Chiarella, C. & Gardini, L. 2011, 'Foreword to the Special Issue of Computational Economics on Complex Dynamics in Economics and Finance', Computational Economics, vol. 38, no. 3, pp. 207-208.
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Chiarella, C., Dieci, R. & He, X. 2011, 'The dynamic behaviour of asset prices in disequilibrium: a survey', International Journal of Behavioural Accounting and Finance, vol. 2, no. 2, pp. 101-139.
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This article surveys boundedly rational heterogeneous agent (BRHA) models of financial markets. We give particular emphasis to the role of the market clearing mechanism used, the utility function of the investors, the interaction of price and wealth dynamics, and calibration of this class of models. Due to agents behavioural features and market noise, the BRHA class of models are both non-linear and stochastic. We show that BRHA models produce both a locally stable fundamental equilibrium corresponding to that of the standard paradigm, as well as instability with a consequent rich range of possible complex behaviours that are analysed by both simulation and deterministic bifurcation analysis. A calibrated model is able to reproduce quite well the stylised facts of financial markets. The BRHA framework seems able to better accommodate market features such as fat tails, volatility clustering, large excursions from the fundamental and bubbles than the standard financial market paradigm.
Cheang, G.H. & Chiarella, C. 2011, 'Exchange Options Under Jump-Diffusion Dynamics', Applied Mathematical Finance, vol. 18, no. 3, pp. 245-276.
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This article extends the exchange option model of Margrabe, where the distributions of both stock prices are log-normal with correlated Wiener components, to allow the underlying assets to be driven by jump-diffusion processes of the type originally introduced by Merton. We introduce the RadonNikody´m derivative process that induces the change of measure from the market measure to an equivalent martingale measure. The choice of parameters in the RadonNikody´m derivative allows us to price the option under different financial-economic scenarios. We also consider American style exchange options and provide a probabilistic interpretation of the early exercise premium.
Chiarella, C., Maina, S.C. & Nikitopoulos-Sklibosios, C. 2011, 'Credit Derivative Pricing with Stochastic Volatility Models'.
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This paper proposes a framework for pricing credit derivatives within the defaultable Markovian HJM framework featuring unspanned stochastic volatility. Motivated by empirical evidence,
hump-shaped level dependent stochastic volatility specifications are proposed, such that the model admits finite dimensional Markovian structures. The model also accommodates a correlation structure
between the stochastic volatility, default-free interest rates and credit spreads. Default free and defaultable bonds are explicitly priced and an approach for pricing credit default swaps and swaptions
is presented where the credit swap rates can be approximated by defaultable bond prices with varying maturities. A sensitivity analysis capturing the impact of the model parameters including correlations
and stochastic volatility, on the credit swap rate and the value of the credit swaption is also presented.
Bischi, G.I., Chiarella, C. & Gardini, L. 2011, 'Foreword to the Special Issue of Computational Economics on Complex Dynamics in Economics and Finance Proceedings of the MDEF (Modelli Dinamici in Economia e Finanza) Workshop, Urbino 23rd-25th September 2010', COMPUTATIONAL ECONOMICS, vol. 38, no. 3, pp. 207-208.
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Asada, T., Chiarella, C., Flaschel, P., Mouakil, T., Proano, C.R. & Semmler, W. 2010, 'Stabilizing an Unstable Economy: On the Choice of Proper Policy Measures', ECONOMICS-THE OPEN ACCESS OPEN-ASSESSMENT E-JOURNAL, vol. 4.
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CHIARELLA, C.A.R.L. & FLASCHEL, P.E.T.E.R. 2010, 'Some Numerical Explorations of the Keynes-Metzler-Goodwin Monetary Growth Model', Indian Economic Review, vol. 45, no. 1, pp. 1-28.
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We study numerically Keynes-Metzler-Goodwin growth, modelling households, firms and government as interacting across real and financial markets. The model allows for sluggish wage / price adjustment, disequilibrium on the market for goods, equilibrium in asset markets and a dynamic government budget restraint. It is first studied in the presence of its intrinsic nonlinearities. Then we add an extrinsic nonlinearity capturing the institutional feature of downward wage rigidity. The dynamic properties of the resulting nonlinear model are studied via bifurcation diagrams, stability basins, by adding stochastic noise to aggregate demand, and by distributional characteristics of key economic quantities.
Chiarella, C., Hung, H. & Flaschel, P. 2010, 'Keynesian Macrodynamics: Convergence, roads to instability and the emergence of complex business fluctuations', AUCO Czech Economic Review, vol. 4, no. 3, pp. 236-262.
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We reformulate the traditional AS-AD growth model, with a Taylor policy rule replacing the conventional LM-curve. The essential features of the model are gradually adjusting wages and prices, perfect foresight on current inflation rates and an adaptive revision of the inflationary climate in which the economy is operating. We compare this approach with the New Keynesian approach with staggered price and wage setting and find that whilst both approaches have common components, they have radically different dynamic implications due to the treatment of the forward-looking part of our wage-price spiral. We show that an estimated version of our model implies local asymptotic stability, due to stable interaction of goods market dynamics with the interest rate policy rule of the central bank, and due to a normal working of a real-wage feedback chain. These results are however endangered when there is a global floor to money wage inflation rates, leading in fact to economic breakdown. In this latter case, the return of some money wage flexibility in deep depressions is of help in restoring the viability of the model, thereby avoiding explosive dynamics and the collapse of the economy.
Chiarella, C. & Duan, J.-.C. 2010, 'Special issue: 2008 Annual Risk Management Conference held in Singapore during June 30-July 2, 2008 Preface', JOURNAL OF ECONOMIC DYNAMICS & CONTROL, vol. 34, no. 11, pp. 2231-2231.
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Chiarella, C. & Szidarovsky, F. 2009, 'Dynamic oligopolies and intertemporal demand interaction', CUBO Matematica Educational, vol. 11, no. 2, pp. 85-105.
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Dynamic oligopolies are examined with continuous time scales and under the assumption that the demand at each time period is affected by earlier demands and consumptions. After the mathematical model is introduced the local asymptotical stability of the equilibrium is examined, and then we will discuss how information delays alter the stability conditions. We will also investigate the occurrence of a Hopf bifurcation gving the possibility of the birth of limit cycles. Numerical examples will be shown toillustrate the theoretical results.
Chiarella, C. & Szidarovsky, F. 2009, 'A multiobjective model of oligopolies under uncertainty', CUBO Matematica Educational, vol. 11, no. 2, pp. 107-115.
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It is assumed that in an n-firm single-product oligopoly without product differentiation the firms face an uncertain price function, which is considered random by the firms. At each time period each firm simultaneously maximizes its expected profit and minimizes the variance of the profit since it wants to receive as high as possible profit with the least possible uncertainty. It is assumed that the best response of each firm is obtained by the weighting method. We show the existence of a unique equilibrium, and investigate the local stability of the equilibrium.
Bhar, R. & Chiarella, C. 2009, 'Inference on forward exchange rate risk premium: Reviewing signal extraction methods', International Journal of Monetary Economics and Finance, vol. 2, no. 2, pp. 115-125.
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The existence of risk premium is thought to be the reason why forward exchange rate is not an unbiased predictor of future spot exchange rate. In this paper we review two methodologies for inferring this unobserved risk premium based upon signal extraction mechanism. One approach relies on the theory of derivatives pricing that relates historical and risk neutral measures via market price of risk. The other approach specifies the risk premium in the historical measure directly. We compare these two methods in predicting future spot exchange rates and contrast these with that of random walk forecast
Chiarella, C. & Szidarovsky, F. 2009, 'Existence and uniqueness in Cournot models with cost externalities', Mathematica Pannonica, vol. 20, no. 1, pp. 17-25.
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In this paper we examine single product Cournot oligopolies, with- out product differentiation, under the assumption that the cost of each firm depends on its own output and also on the output of the rest of the industry. The competition of the firms on the secondary market for manpower, capital, energy, and so forth as well as the spillover effect of the R&D investments of the firms can be taken into account with this more general cost structure. The existence of a unique NashCournot equilibrium is proved under realistic conditions. Our result is a straightforward generalization of the well-known existence and uniqueness theorem of concave oligopolies.
Chiarella, C., Kang, B., Meyer, G. & Ziogas, A. 2009, 'The evaluation of American option prices under stochastic volatility and jump diffusion dynamics using the method of lines', International Journal of Theoretical and Applied Finance, vol. 12, no. 3, pp. 393-425.
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This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston [18], and by a Poisson jump process of the type originally introduced by Merton [25]. We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer [26] for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen and Toivanen [21]. The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation and which is taken as the benchmark for the price. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered.
Zhu, M., Chiarella, C., He, X.-.Z. & Wang, D. 2009, 'Does the market maker stabilize the market?', Physica A: Statistical Mechanics and its Applications, vol. 388, no. 15-16, pp. 3164-3180.
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The market maker plays an important role in price formation, but his/her behavior and stabilizing impact on the market are relatively unclear, in particular in speculative markets. This paper develops a financial market model that examines the impact on market stability of the market maker, who acts as both a liquidity provider and an active investor in a market consisting of two types of boundedly rational speculative investors-the fundamentalists and trend followers. We show that the market maker does not necessarily stabilize the market when he/she actively manages the inventory to maximize profits, and that rather the market maker's impact depends on the behavior of the speculators. Numerical simulations show that the model is able to generate outcomes for asset returns and market inventories that are consistent with empirical findings. © 2009.
Chiarella, C., Fanelli, V. & Musti, S. 2009, 'Modelling the Evolution of Credit Spreads Using the Cox Process Within the HJM Framework A CDS Option Pricing Model'.
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In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic
intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default
swap option price in a probability setting equipped with a sub filtration structure. The Euler-Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical
algorithm for pricing. Finally, the Antithetic Variable technique is used to reduce the variance of credit default swap option prices.
Chiarella, C., Iori, G. & Perello, J. 2009, 'The impact of heterogeneous trading rules on the limit order book and order flows', Journal of Economic Dynamics and Control, vol. 33, no. 3, pp. 525-537.
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In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. Agents are assumed to have three components of the expectation of future asset returns, namely fundamentalist, chartist and noise trader. Furthermore agents differ in the characteristics describing these components, such as time horizon, risk aversion and the weights given to the various components. The model developed here extends a great deal of earlier literature in that the order submissions of agents are determined by utility maximisation, rather than the mechanical unit order size that is commonly assumed. In this way the order flow is better related to the ongoing evolution of the market. For the given market structure we analyze the impact of the three components of the trading strategies on the statistical properties of prices and order flows and observe that it is the chartist strategy that is mainly responsible of the fat tails and clustering in the artificial price data generated by the model. The paper provides further evidence that large price changes are likely to be generated by the presence of large gaps in the book.
Chiarella, C., Hung, H. & To, T. 2009, 'The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach', Computational Statistics and Data Analysis, vol. 53, no. 6, pp. 2075-2088.
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The dynamics for interest rate processes within the well-known multi-factor Heath, Jarrow and Morton (HJM) specification are considered. Despite the flexibility of and the notable advances in theoretical research about the HJM model, the number of empirical studies of it is still very sparse. This paucity is principally due to the difficulties in estimating models in this class, which are not only high-dimensional, but also nonlinear and involve latent state variables. The estimation of a fairly broad class of HJM models as a nonlinear filtering problem is undertaken by adopting the local linearization filter, which is known to have some desirable statistical and numerical features, so enabling the estimation of the model via the maximum likelihood method. The estimator is then applied to the US, the UK and the Australian markets. Different two- and three-factor models are found to be the best for each market, with the factors being the level, the slope and the twist effect. The contribution of each factor towards overall variability of the interest rates and the financial reward each factor claims are found to differ considerably from one market to another.
Chiarella, C. & Ziogas, A. 2009, 'American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach', Applied Mathematical Finance, vol. 16, no. 1, pp. 37-79.
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We consider the American option pricing problem in the case where the underlying asset follows a jump-diffusion process. We apply the method of Jamshidian to transform the problem of solving a homogeneous integro-partial differential equation (IPDE) on a region restricted by the early exercise (free) boundary to that of solving an inhomogeneous IPDE on an unrestricted region. We apply the Fourier transform technique to this inhomogeneous IPDE in the case of a call option on a dividend paying underlying to obtain the solution in the form of a pair of linked integral equations for the free boundary and the option price. We also derive new results concerning the limit for the free boundary at expiry. Finally, we present a numerical algorithm for the solution of the linked integral equation system for the American call price, its delta and the early exercise boundary. We use the numerical results to quantify the impact of jumps on American call prices and the early exercise boundary.
Chiarella, C., Dieci, R., Gardini, L. & Sbragia, L. 2008, 'A model of financial market dynamics with heterogeneous beliefs and state-dependent confidence', Computational Economics, vol. 32, no. 1-2, pp. 55-72.
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In a simple model of financial market dynamics, we allow the price of a risky security to be set by a market maker depending on the excess demand of heterogeneous interacting traders, fundamentalists and chartists, who place their orders based upon different expectations schemes about future prices: while chartists rely on standard trend-based rules, fundamentalists are assumed to know the economic environment and to form their beliefs accordingly. As price moves away from the long-run fundamental, fundamentalists become less confident in their forecasts, and put increasing weight on a reversion towards the fundamental price. The resulting two-dimensional discrete time dynamical system can exhibit a rich range of dynamic scenarios, often characterized by coexistence of attractors. A simple noisy version of the model reveals a variety of possible patterns for return time series. © Springer Science+Business Media, LLC. 2008.
Chiarella, C., He, X.-.Z., Wang, D. & Zheng, M. 2008, 'The stochastic bifurcation behaviour of speculative financial markets', Physica A: Statistical Mechanics and its Applications, vol. 387, no. 15, pp. 3837-3846.
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This paper establishes a continuous-time stochastic asset pricing model in a speculative financial market with fundamentalists and chartists by introducing a noisy fundamental price. By application of stochastic bifurcation theory, the limiting market equilibrium distribution is examined numerically. It is shown that speculative behaviour of chartists can cause the market price to display different forms of equilibrium distributions. In particular, when chartists are less active, there is a unique equilibrium distribution which is stable. However, when the chartists become more active, a new equilibrium distribution will be generated and become stable. The corresponding stationary density will change from a single peak to a crater-like density. The change of stationary distribution is characterized by a bimodal logarithm price distribution and fat tails. The paper demonstrates that stochastic bifurcation theory is a useful tool in providing insight into various types of financial market behaviour in a stochastic environment. © 2008 Elsevier Ltd. All rights reserved.
Chiarella, C. & Szidarovszky, F. 2008, 'Dynamic oligopolies with production adjustment costs', Scientia Iranica, vol. 15, no. 1, pp. 120-124.
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Single-product oligopolies, without product differentiation, are examined under the assumption that any increase in production levels has additional cost to the firms. Therefore, the best response of each firm depends on the current output of the rest of the industry and on the previous output of the firm. Two dynamic models are introduced. In the first case, the firms form adaptive expectations on the output of the rest of the industry and select the best response output levels and, in the second case, it is assumed that they adjust their output levels adaptively. Conditions are derived in both cases for the asymptotic stability of the equilibrium. © Sharif University of Technology, February 2008.
Roethig, A. & Chiarella, C. 2007, 'Investigating nonlinear speculation in cattle, corn, and hog futures markets using logistic smooth transition regression models', JOURNAL OF FUTURES MARKETS, vol. 27, no. 8, pp. 719-737.
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Chiarella, C., Hsiao, C.-.Y. & Semmler, W. 2007, 'Intertemporal asset allocation when the underlying factors are unobservable', Computational Economics, vol. 29, no. 3-4, pp. 383-418.
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The defaultable forward rate is modelled as a jump diffusion process within the Schonbucher [26,27] general Heath, Jarrow and Morton [20] framework where jumps in the defaultable term structure fd(t, T) cause jumps and defaults to the defaultable bond prices Pd(t, T). Within this framework, we investigate an appropriate forward rate volatility structure that results in Markovian defaultable spot rate dynamics. In particular, we consider state dependent Wiener volatility functions and time dependent Poisson volatility functions. The corresponding term structures of interest rates are expressed as finite dimensional affine realizations in terms of benchmark defaultable forward rates In addition, we extend this model to incorporate stochastic spreads by allowing jump intensities to follow a square-root diffusion process. In that case the dynamics become non-Markovian and to restore path independence we propose either an approximate Markovian scheme or, alternatively, constant Poisson volatility functions. We also conduct some numerical simulations to gauge the effect of the stochastic intensity and the distributional implications of various volatility specifications.
Engel, A., Szidarovszky, F. & Chiarella, C. 2007, 'A Game Theoretical Coalition Model of International Fishing with Time Delay', Journal of Concrete and Applicable Mathematics, vol. 5, no. 2, pp. 115-131.
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The oligopoly model of international fishing of Szidarovszky and Okuguchi [7] where the harvesting countries form a coalition is re- visited with the additional assumption that there is a time lag in obtaining and implementing information on the fish stock. The introduction of continuously distributed time lags results in a special Volterra-type integro-differential equation. Since it is equivalent to a system of nonlinear ordinary differential equations, linearization and standard techniques are used to examine the local asymptotic behavior of the equilibrium. Stability conditions are derived and in the case of instability special cyclic behavior is analyzed.
This paper examines the pricing of interest rate derivatives when the interest rate dynamics experience infrequent jump shocks modelled as a Poisson process. The pricing framework adapted was developed by Chiarella and Nikitopoulos to provide an extension of the Heath, Jarrow and Morton model to jump-diffusions and achieves Markovian structures under certain volatility specifications. Fourier Transform solutions for the price of a bond option under deterministic volatility specifications are derived and a control variate numerical method is developed under a more general state dependent volatility structure, a case in which closed form solutions are generally not possible. In doing so, a novel perspective is provided on control variate methods by going outside a given complex model to a simpler more tractable setting to provide the control variates.
Chiarella, C., Dieci, R. & He, X. 2007, 'Heterogeneous Expectations and Speculative Behavior in a Dynamic Multi-Asset Framework', Journal of Economic Behavior and Organization, vol. 62, no. 3, pp. 408-427.
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This paper develops a dynamic model of a financial market where heterogeneous agents invest among multiple risky assets and a risk-free asset, under a market maker scenario. Particular attention is paid to the case of two risky assets and two agent types, fundamentalists and trend chasers, whose beliefs on both first and second moments of the conditional distribution of returns are based on past observations. Conditions for the stability of the ?fundamental? equilibrium are established and the effect of the correlation between the risky assets is examined. It turns out that investors? anticipated correlation and dynamic portfolio diversification do not always have a stabilizing role, but rather may act as a source of complexity in the financial market.
Rothig, A. & Chiarella, C. 2007, 'Investigating Nonlinear Speculation in Cattle, Corn and Hog Futures Markets Using Logisitic Smooth Transition Regression Models', Journal Of Futures Markets, vol. 27, no. 8, pp. 719-737.
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This study explores nonlinearities in the response of speculators? trading activity to price changes in live cattle, corn, and lean hog futures markets Analyzing weekly data from March 4, 1997 through December 27, 2005, the authors reject linearity in all of these markets. Using smooth transition regression models, the authors found a similar structure of nonlinearities with regard to the number of different regimes, the choice of the transition variable, and the value at which the transition occurs.
Chiarella, C., He, X.-.Z. & Wang, D. 2006, 'A behavioral asset pricing model with a time-varying second moment', Chaos, Solitons and Fractals, vol. 29, no. 3, pp. 535-555.
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We develop a simple behavioral asset pricing model with fundamentalists and chartists in order to study price behavior in financial markets when chartists estimate both conditional mean and variance by using a weighted averaging process. Through a stability, bifurcation, and normal form analysis, the market impact of the weighting process and time-varying second moment are examined. It is found that the fundamental price becomes stable (unstable) when the activities from both types of traders are balanced (unbalanced). When the fundamental price becomes unstable, the weighting process leads to different price dynamics, depending on whether the chartists act as either trend followers or contrarians. It is also found that a time-varying second moment of the chartists does not change the stability of the fundamental price, but it does influence the stability of the bifurcations. The bifurcation becomes stable (unstable) when the chartists are more (less) concerned about the market risk characterized by the time-varying second moment. Different routes to complicated price dynamics are also observed. The analysis provides an analytical foundation for the statistical analysis of the corresponding stochastic version of this type of behavioral model. © 2005 Elsevier Ltd. All rights reserved.
Despite the pervasiveness of the efficient markets paradigm in the academic finance literature, the use of various moving average (MA) trading rules remains popular with financial market practitioners. This paper proposes a stochastic dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long-run) MA. Our simulations show that the MA is a source of market instability, and the interaction of the MA and market noises can lead to the tendency for the market price to take long excursions away from the fundamental. The model reveals various market price phenomena, the coexistence of apparent market efficiency and a large chartist component, price resistance levels, long memory and skewness and kurtosis of returns. © 2006 Elsevier B.V. All rights reserved.
Chiarella, C. & Hsiao, C.-.Y. 2006, 'The Impact of Short-Sale Constraints on Asset Allocation Strategies via the Backward Markov Chain Approximation Method', Computational Economics, vol. 28, no. 2, pp. 113-137.
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Asada, T., Chen, P., Chiarella, C. & Flaschel, P. 2006, 'Keynesian dynamics and the wage-price spiral: A baseline disequilibrium model', JOURNAL OF MACROECONOMICS, vol. 28, no. 1, pp. 90-130.
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Agliari, A., Chiarella, C. & Gardini, L. 2006, 'A re-evaluation of adaptive expectations in light of global nonlinear dynamic analysis', JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION, vol. 60, no. 4, pp. 526-552.
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Chiarella, C., Dieci, R. & Gardini, L. 2006, 'Asset price and wealth dynamics in a financial market with heterogeneous agents', Journal of Economic Dynamics and Control, vol. 30, no. 9-10, pp. 1755-1786.
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This paper considers a discrete-time model of a financial market with one risky asset and one risk-free asset, where the asset price and wealth dynamics are determined by the interaction of two groups of agents, fundamentalists and chartists. In each per
Chiarella, C. 2006, 'My chaotic career - from billiard balls to economic dynamics and financial markets - Carl Chiarella', CHAOS SOLITONS & FRACTALS, vol. 29, no. 3, pp. 517-519.
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Chiarella, C. & Ziogas, A. 2006, 'A fourier transform analysis of the American call option on assets driven by jump-diffusion processes (QFRC paper #174)', Quantitative Finance Research Centre Working Paper Series, vol. 174.
Chen, P., Chiarella, C., Flaschel, P. & Semmler, W. 2006, 'Keynesian macrodynamics and the Phillips cuve: An estimated baseline macromodel for the US economy (F&E paper #147)', School of Finance & Economics Working Paper Series, vol. 147.
Chen, P., Chiarella, C., Flaschel, P. & Hung, H. 2006, 'Keynesian disequilibrium dynamics: Covergence roads to instability and the emergence of complex business (F&E paper #146)', School of Finance & Economics Working Paper Series, vol. 146.
Rothig, A. & Chiarella, C. 2006, 'Investigating non-linear speculation in cattle, corn and hog futures markets using logistics smooth transition regression models (CEM paper #101)', Centre for Empirical Macroeconomics, University of Bielefeld Working Paper Series, vol. 101.
Rothig, A. & Chiarella, C. 2006, 'Investigating non-linear speculation in cattle, corn and hog futures markets using logistics smooth transition regression models (IE paper #167)', Institute of Economics, Technical University of Darmstadt Working Paper Series, vol. 167.
CHIARELLA, C.A.R.L., FLASCHEL, P.E.T.E.R. & HUNG, H.I.N.G. 2006, 'INTERACTING BUSINESS CYCLE FLUCTUATIONS: A TWO-COUNTRY MODEL', The Singapore Economic Review, vol. 51, no. 03, pp. 365-394.
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Bhar, R., Chiarella, C., Hung, H. & Runggaldier, W.J. 2006, 'The volatility of the instantaneous spot interest rate implied by arbitrage pricing - A dynamic Bayesian approach', AUTOMATICA, vol. 42, no. 8, pp. 1381-1393.
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Chen, P., Chiarella, C., Flaschel, P. & Semmler, W. 2006, 'The feedback channels in macroeconomics: analytical foundations for structural econometric model building', Central European Journal of Operations Research, vol. 14, no. 3, pp. 261-288.
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We investigate important macroeconomic and macroeconometric feedback channels in models that concern the dynamic interaction of the labor market, product market and the monetary and financial sector. The core of our study is an applied disequilibrium model of monetary growth of a small open economy. After surveying the feedback channels we consider a compact description of the intensive form of the model. We consider various types of subsystems, the integration of which is subsequently compared from the perspective of bifurcation diagrams that separate cases of asymptotic stability from stable cyclical behavior as well as pure explosiveness. In this way we lay out a research strategy, which will show, in contrast to what is generally believed, that applied integrated macrodynamic systems can have a variety of interesting attractors and transient dynamics, which are obtained in particular when locally explosive situations are turned into bounded dynamics by the addition of specifically tailored extrinsic nonlinearities.
Chiarella, C., He, X.-.Z., Hung, H. & Zhu, P. 2006, 'An analysis of the cobweb model with boundedly rational heterogeneous producers', Journal of Economic Behavior and Organization, vol. 61, no. 4, pp. 750-768.
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This paper considers the traditional cobweb model with heterogenous risk averse producers whose supply functions involve their estimates of the conditional mean and variance of the future price. The producers seek to learn these quantities by applying geometric decay processes (GDP) to past prices. The heterogeneity manifests itself in the lag lengths and memory parameters applied to past prices as well as in risk aversion coefficients. We find that each dimension of heterogeneity changes/enriches the cobweb dynamics with respect to the case of homogeneous producers. © 2006 Elsevier B.V. All rights reserved.
Chiarella, C. & Tô, T.-.D. 2006, 'The Multifactor Nature of the Volatility of Futures Markets', Computational Economics, vol. 27, no. 2-3, pp. 163-183.
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CHIARELLA, C.A.R.L., FLASCHEL, P.E.T.E.R. & HUNG, H.I.N.G. 2006, 'INTERACTING BUSINESS CYCLE FLUCTUATIONS: A TWO-COUNTRY MODEL', The Singapore Economic Review, vol. 51, no. 03, pp. 365-394.
In this paper, we develop a model of business cycle fluctuations between two interacting open economies within the disequilibrium or non-market clearing paradigm. We analyze the main feedback mechanisms (Keynes, Mundell, Rose and Dornbusch) driving the dynamics and the conflict between their stabilizing and destabilizing tendencies and how these depend on certain key speeds of adjustment in the real and foreign exchange sectors. We explore numerically a variety of situations of interacting price cycles in the two countries, where the steady state is locally repelling, but where the overall dynamics are bounded in an economically meaningful domain by assuming downward money wage rigidity.
Chiarella, C. & Ziogas, A. 2005, 'Evaluation of American strangles', Journal Of Economic Dynamics & Control, vol. 29, no. 1-2, pp. 31-62.
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This paper presents a generalisation of McKean's free boundary value problem for American options by considering an American strangle position, where exercising one side of the payoff early knocks-out the remaining side. The Fourier transform technique i
Chiarella, C. & Szidarovszky, F. 2005, 'On the stability of price-adjusting oligopolies with incomplete information', INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE, vol. 36, no. 8, pp. 501-507.
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Chiarella, C., Dieci, R. & Gardini, L. 2005, 'The dynamic interaction of speculation and diversification', Applied Mathematical Finance, vol. 12, no. 1, pp. 17-52.
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A discrete time model of a financial market is developed, in which heterogeneous interacting groups of agents allocate their wealth between two risky assets and a riskless asset. In each period each group formulates its demand for the risky assets and the risk-free asset according to myopic mean-variance maximizazion. The market consists of two types of agents: fundamentalists, who hold an estimate of the fundamental values of the risky assets and whose demand for each asset is a function of the deviation of the current price from the fundamental, and chartists, a group basing their trading decisions on an analysis of past returns. The time evolution of the prices is modelled by assuming the existence of a market maker, who sets excess demand of each asset to zero at the end of each trading period by taking an offsetting long or short position, and who announces the next period prices as functions of the excess demand for each asset and with a view to long-run market stability. The model is reduced to a seven-dimensional nonlinear discrete-time dynamical system, that describes the time evolution of prices and agents' beliefs about expected returns, variances and correlation. The unique steady state of the model is determined and the local asymptotic stability of the equilibrium is analysed, as a function of the key parameters that characterize agents' behaviour. In particular it is shown that when chartists update their expectations sufficiently fast, then the stability of the equilibrium is lost through a supercritical Neimark-Hopf bifurcation, and self-sustained price fluctuations along an attracting limit cycle appear in one or both markets. Global analysis is also performed, by using numerical techniques, in order to understand the role played by the chartists' behaviour in the transition to a regime characterized by irregular oscillatory motion and coexistence of attractors. It is also shown how changes occurring in one market may affect the price dynamics o...
Chiarella, C. & Platen, E. 2005, 'Special issue: Introduction to Selected Proceedings from the Quantitative Methods in Finance 2004 Conference (QMF 2004)', QUANTITATIVE FINANCE, vol. 5, no. 3, pp. 235-235.
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Chiarella, C., Clewlow, L. & Musti, S. 2005, 'A volatility decomposition control variate technique for Monte Carlo simulations of Heath Jarrow Morton models', European Journal of Operational Research, vol. 161, no. 2, pp. 325-336.
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The aim of this work is to develop a simulation approach to the yield curve evolution in the Heath, Jarrow and Morton [Econometrica 60 (1) (1992) 77] framework. The stochastic quantities considered as affecting the forward rate volatility function are the spot rate and the forward rate. A decomposition of the volatility function into a Hull and White [Rev. Financial Stud. 3 (1990) 573] volatility and a remainder allows us to develop an efficient Control Variate Method that makes use of the closed form solution of the Hull and White call option. This technique considerably speeds up the simulation algorithm to approximate call option values with Monte Carlo simulation. © 2003 Elsevier B.V. All rights reserved.
Chiarella, C. & Szidarovszky, F. 2005, 'Cournot oligopolies with product differentiation under uncertainty', Computers & Mathematics with Applications, vol. 50, no. 3-4, pp. 413-424.
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Bohm, V. & Chiarella, C. 2005, 'Mean variance preferences expectations formation and the dynamics of random asset prices', Mathematical Finance, vol. 15, no. 1, pp. 61-97.
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This paper analyzes the dynamics of an explicit random process of prices and price expectations of finitely many assets in an economy with overlapping generations of heterogeneous consumers. They maximize expected utility with respect to subjective trans
The use of various moving average (MA) rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents employ technical trading rules of the type used in practice. In this paper we propose a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long-run) MA. Both types of traders are boundedly rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag length used for the MA. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different MA rules. The price dynamics of the moving average rule are also examined and one of our main findings is that an increase of the window length of the MA rule can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden market crashes, price resistance and price switching between different levels.
Chiarella, C. & Szidarovszky, F. 2005, 'Cournot oligopolies with product differentiation under uncertainty', Computers and Mathematics with Applications, vol. 50, no. 3-4, pp. 413-424.
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This paper considers Cournot oligopolies with product differentiation when the firms have inexact knowledge of the price functions and there are random time lags in obtaining and implementing information on the firms' own outputs and prices as well as on the prices of the competitors. After the basic dynamic model without time lag is formulated, the asymptotic stability in the linear case is examined. The introduction of time lags makes the asymptotic behaviour of the steady state more complex. A detailed stability analysis is undertaken. In the case of symmetric firms and with a special weighting function, the possibility of the birth of limit cycle motion in output is also investigated in addition to stability analysis. © 2005 Elsevier Ltd. All rights reserved.
Szidarovszky, F., Engel, A. & Chiarella, C. 2004, 'A game theoretical model of international fishing with time delay', International Game Theory Review, vol. 6, no. 3, pp. 391-415.
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This paper studies the evolution of a fish stock that is exploited by an n-country oligopoly. A feature of the economic structure is that the countries exploiting the fish stock experience time lags in obtaining and implementing information on the fish stock. The local asymptotic behavior of the equilibrium is analyzed, including asymptotic stability, instability, and cyclical behavior. Under the assumption of symmetric countries, two special cases are examined in detail. In the first case identical time delays are assumed, and in the second case it is assumed that one country has a different time delay from the others. This semi-symmetric case gives some insight into the consequence of asymmetry of the countries on the asymptotic behavior of the fish stock.
Chiarella, C. & Gao, S. 2004, 'The value of the S&P 500A macro view of the stock market adjustment process', Global Finance Journal, vol. 15, no. 2, pp. 171-196.
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Bischi, G.-.I., Chiarella, C. & Kopel, M. 2004, 'The long run outcomes and global dynamics of a duopoly game with misspecified demand functions', International Game Theory Review, vol. 6, no. 3, pp. 343-379.
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In this paper we study a model of a quantity-setting duopoly market where firms lack knowledge of the market demand. Using a misspecified demand function firms determine their profit-maximizing choices of their corresponding perceived market game. For illustrative purposes we assume that the (true) demand function is linear and that the reaction functions of the players are quadratic. We then investigate the global dynamics of this game and characterize the number of steady states and their welfare properties. We study the basins of attraction of these steady states and present situations in which global bifurcations of their basins occur when model parameters are varied. The economic significance of our result is to show that in situations where players choose their actions based on a misspecified model of the environment, additional self-confirming steady states may emerge, despite the fact that the Nash-equilibrium of the game under perfect knowledge is unique. As a consequence the long run outcome of the game and overall welfare is highly dependent upon initial conditions.
Agliari, A., Chiarella, C. & Gardini, L. 2004, 'A stability analysis of the perfect foresight map in nonlinear models of monetary dynamics', CHAOS SOLITONS & FRACTALS, vol. 21, no. 2, pp. 371-386.
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Chiarella, C. & Szidarovszky, F. 2004, 'Dynamic oligopolies without full information and with continuously distributed time lags', JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION, vol. 54, no. 4, pp. 495-511.
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Szidarovszky, F. & Chiarella, C. 2004, 'The asymptotic behavior of dynamic producer-consumer systems', Mathematical and Computer Modelling, vol. 39, no. 11-12, pp. 1297-1312.
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Dynamic Arrow-type price dynamics are investigated in a continuous time framework. The existence of a unique equilibrium is first proved under realistic conditions. Then, the local asymptotic stability of the equilibrium in the presence of instantaneous price and output information is shown. Continuously distributed time lags are then assumed in obtaining and implementing price and output information, or equivalently, it may be assumed that the firms and/or the market wants to react to long term effects rather than to follow sudden changes in price or outputs. If a time lag is assumed only in estimating the demand in the market, then the local asymptotic stability of the equilibrium is preserved. If the producers also use delayed information, then instability may occur. Stability conditions are derived and in the case of bifurcation the possibility of the birth of limit cycles is explored. © 2004 Elsevier Ltd. All rights reserved.
Bhar, R., Chiarella, C. & Runggaldier, W.J. 2004, 'Inferring the forward looking equity risk premium from derivative prices', STUDIES IN NONLINEAR DYNAMICS AND ECONOMETRICS, vol. 8, no. 1.
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Engel, A., Szidarovszky, F. & Chiarella, C. 2003, 'A game theoretical partially cooperative model of international fishing with time delay', Chaos, Solitons and Fractals, vol. 18, no. 3, pp. 549-560.
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A common generalization of the oligopoly model of international fishing of Szidarovszky and Okuguchi [Seoul J. Econom. 11 (1998) 321] and the grand coalition model of international fishing of Szidarovszky and Okuguchi [Seoul J. Econom. 13 (2000) 471] is introduced to consider the case of partial cooperation among the fishing countries. Then, the assumption that there is a time lag in obtaining and implementing information on the fish stock is added. Similarly to the study of Engel et al. [Proceedings of the 2001 IEEE International Conference on Systems, Man and Cybernetics, Tucson, Arizona, October 7-10, 2001, 2001, p. 2658] continuously distributed time lags are considered. The local asymptotical stability of the equilibrium is analyzed, and in the case of loss of stability the possibility of the birth of limit cycles is explored. © 2003 Elsevier Science Ltd. All rights reserved.
Chiarella, C. & Szidarovszky, F. 2003, 'Bounded continuously distributed delays in dynamic oligopolies', CHAOS SOLITONS & FRACTALS, vol. 18, no. 5, pp. 977-993.
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Chiarella, C., Flaschel, P., Gong, G. & Semmler, W. 2003, 'Nonlinear Phillips curves, complex dynamics and monetary policy in a Keynesian macro model', CHAOS SOLITONS & FRACTALS, vol. 18, no. 3, pp. 613-634.
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Chiarella, C. & To, T. 2003, 'The jump component of the volatility structure of interest rate futures markets: an international comparison', Journal Of Futures Markets, vol. 23, no. 12, pp. 1125-1158.
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Chiarella, C. & Szidarovszky, F. 2003, 'Dynamic oligopolies with pollution treatment cost sharing', Keio Economics Studies, vol. XL, no. 1, pp. 27-44.
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We analyse the Bouchouev integral equation for the deterministic volatility function in the Black-Scholes option pricing model. We areable to reduce Bouchouev's original triple integral equation to a single integral equation and describe its numerical solution. Moreover we show empirically that the most complex term in the equation may often be safely ignored for the purposes of numerical calculations. We present a selection of numerical examples indicating the range of time values for which we would expect the equation to be valid. © 2003 Kluwer Academic Publishers.
Chiarella, C., Flaschel, P., Groh, G. & Semmler, W. 2003, 'Reply to K. Velupillai's review of Chiarella and Flaschel: The dynamics of Keynesian monetary growth: Macro foundations (CF), and Chiarella, Flaschel, Groh and Semmler: Disequilibrium, growth and labor market dynamics: Macro perspectives (CFGS) - Introduction: The historical perspective', JOURNAL OF ECONOMICS-ZEITSCHRIFT FUR NATIONALOKONOMIE, vol. 78, no. 1, pp. 96-104.
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Chiarella, C., Gallegati, M., Leombruni, R. & Palestrini, A. 2003, 'Asset price dynamics among heterogeneous interacting agents', Computational Economics, vol. 22, no. 2-3, pp. 213-223.
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Chiarella, C. & He, X.Z. 2003, 'Dynamics of beliefs and learning under a(L)-processes - the heterogeneous case', JOURNAL OF ECONOMIC DYNAMICS & CONTROL, vol. 27, no. 3, pp. 503-531.
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Chiarella, C. & Kwon, O. 2003, 'Finite dimensional affine realisation of HJM models in terms of forward rates and yields', Review of Derivatives Research, vol. 6, no. 2, pp. 129-155.
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Li, W., Rychlik, M., Szidarovszky, F. & Chiarella, C. 2003, 'On the attractivity of a class of homogeneous dynamic economic systems', Nonlinear Analysis, Theory, Methods and Applications, vol. 52, no. 6, pp. 1617-1636.
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The attractivity properties of the set of equilibria of a special class of homogeneous dynamic economic systems are examined. The nonlinearity of the models and the presence of eigenvalues with zero real parts make the application of the classical theory impossible. Some principles of the modern theory of dynamical systems and invariant manifolds are applied, and the local attractivity of the set of equilibria is verified under mild conditions. As an application, special labor-managed oligopolies are investigated. © 2003 Elsevier Science Ltd. All rights reserved.
Chiarella, C. & Platen, E. 2003, 'Introduction to Selected Proceedings from Quantitative Methods in Finance 2002', QUANTITATIVE FINANCE, vol. 3, no. 1, pp. C5-C5.
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Trade among individuals occurs either because tastes (risk aversion)differ, endowments differ, or beliefs differ. Utilising the concept of'adaptively rational equilibrium' and a recent framework of Brock and Hommes[6, 7] this paper incorporates risk and learning schemes into a simplediscounted present value asset price model with heterogeneous beliefs. Agentshave different risk aversion coefficients and adapt their beliefs (aboutfuture returns) over time by choosing from different predictors orexpectations functions, based upon their past performance as measured byrealized profits. By using both bifurcation theory and numerical analysis, itis found that the dynamics of asset pricing is affected by the relative riskattitudes of different types of investors. It is also found that the externalnoise and learning schemes can significantly affect the dynamics. Comparedwith the findings of Brock and Hommes [7] on the dynamics caused by change ofthe intensity of choice to switch predictors, it is found that many of theirinsights are robust to the generalizations considered: however, the resultingdynamical behavior is considerably enriched and exhibits some significantdifferences. © 2002 Kluwer Academic Publishers.
Chiarella, C. & Szidarovszky, F. 2002, 'The asymptotic behavior of dynamic rent-seeking games', Computers and Mathematics with Applications, vol. 43, no. 1-2, pp. 169-178.
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Dynamic rent-seeking games with nonlinear cost functions are analyzed. The local asymptotic stability of the solution is first examined. We show that in the absence of a dominant agent, all eigenvalues of the Jacobian are real. Conditions are given for the local asymptotic stability as well as for the local instability of the equilibrium. In the presence of a dominant agent, complex eigenvalues are possible. Simple stability conditions are presented for cases when all eigenvalues are real, and the possibility of limit cycles is analyzed in the case of complex eigenvalues.
Chiarella, C. & Iori, G. 2002, 'A simulation analysis of the microstructure of double auction markets*', Quantitative Finance, vol. 2, no. 5, pp. 346-353.
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Chiarella, C., Semmler, W., Mittnik, S. & Zhu, P. 2002, 'Stock market, interest rate and output: a model and estimation for US time series data', Studies in NonLinear Dynamics and Econometrics, vol. 6, no. 1 / Article 2, pp. 1-37.
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Stock market, interest rate and output: a model and estimation for US time series data
Chiarella, C., Dieci, R. & Gardini, L. 2002, 'Speculative behaviour and complex asset price dynamics: a global analysis', JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION, vol. 49, no. 2, pp. 173-197.
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Chiarella, C. 2002, 'Attractors, bifurcations, and chaos. Nonlinear phenomena in economics.', JOURNAL OF ECONOMICS-ZEITSCHRIFT FUR NATIONALOKONOMIE, vol. 75, no. 2, pp. 186-189.
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Chiarella, C. & Kwon, O.K. 2001, 'Classes of interest rate models under the HJM framework', Asia-Pacific Financial Markets, vol. 8, no. 1, pp. 1-22.
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Although the HJM term structure model is widely accepted as the most general, and perhaps the most consistent, framework under which to study interest rate derivatives, the earlier models of Vasicek, Cox-Ingersoll-Ross, Hull-White, and Black-Karasinski remain popular among both academics and practitioners. It is often stated that these models are special cases of the HJM framework, but the precise links have not been fully established in the literature. By beginning with certain forward rate volatility processes, it is possible to obtain classes of interest models under the HJM framework that closely resemble the traditional models listed above. Further, greater insight into the dynamics of the interest rate process emerges as a result of natural links being established between the model parameters and market observed variables. © 2001 Kluwer Academic Publishers.
Chiarella, C., Flaschel, P., Franke, R. & Semmler, W. 2001, 'Output Interest & the Stock Market: An Alternative to the Jump Variable Technique', The Bulletin of the Czech Econometric Society, vol. 7, no. 13, pp. 1-29.
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Szidarovszky, F. & Chiarella, C. 2001, 'Dynamic Oligopilies, Stability & Bifurcation', CUBO Matematica Educational, vol. 3, no. 2, pp. 269-284.
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Chiarella, C., Dieci, R. & Gardini, L. 2001, 'Asset price dynamics in a financial market with fundamentalists and chartists', DISCRETE DYNAMICS IN NATURE AND SOCIETY, vol. 6, no. 2, pp. 69-+.
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Chiarella, C., Pasquali, S. & Runggaldier, W.J. 2001, 'On filtering in Markovian term structure models: An approximation approach', Advances in Applied Probability, vol. 33, no. 4, pp. 794-809.
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We consider a parametrization of the Heath-Jarrow-Morton (HJM) family of term structure of interest rate models that allows a finite-dimensional Markovian representation of the stochastic dynamics. This parametrization results from letting the volatility function depend on time to maturity and on two factors: the instantaneous spot rate and one fixed-maturity forward rate. Our main purpose is an estimation methodology for which we have to model the observations under the historical probability measure. This leads us to consider as an additional third factor the market price of interest rate risk, that connects the historical and the HJM martingale measures. Assuming that the information comes from noisy observations of the fixed-maturity forward rate, the purpose is to estimate recursively, on the basis of this information, the three Markovian factors as well as the parameters in the model, in particular those in the volatility function. This leads to a nonlinear filtering problem, for the solution of which we describe an approximation methodology, based on time discretization and quantization. We prove the convergence of the approximate filters for each of the observed trajectories.
Chiarella, C. & Szidarovszky, F. 2001, 'The Nonlinear Cournot Model Under Uncertainty with Continously Distributed Time Lags', Central European Journal of Operational Research, vol. 9, pp. 183-196.
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Bhar, R., Chiarella, C. & Pham, T.M. 2001, 'Modelling the currency forward risk premium: A new perspective', Asia-Pacific Financial Markets, vol. 8, no. 4, pp. 341-360.
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In this paper we seek to develop a new approach to the time series analysis of foreign exchange risk premia. We do so by assuming a geometric Brownian process for the spot exchange rate and expressing the no-arbitrage spot-forward price relationship under the historical probability measure. We are thereby able to obtain a stochastic differential equation system linking the spot exchange rate, the forward exchange rate and the risk premium (modelled directly as a mean-reverting diffusion process) which we estimate using Kalman filtering techniques. We are able to use observations at a range of frequencies since the framework we set up does not involve overlapping observations. The model is then applied to the French Franc/USD, DEM/USD, GBP/USD, and Japanese Yen/USD exchange rates from 1 January 1990 to 31 December 1998. For all currencies we find evidence that the forward risk premium is stationary and exhibits substantial positive time variation. © 2002 Kluwer Academic Publishers.
Chiarella, C. & Kwon, O.K. 2001, 'Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model', Finance and Stochastics, vol. 5, no. 2, pp. 237-257.
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Chiarella, C. & Kwon, O.K. 2001, 'Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model', vol. 5, no. 2, pp. 237-257.
In this paper, a class of forward rate dependent Markovian transformations of the Heath-Jarrow-Morton [16] term structure model are obtained by considering volatility processes that are solutions of linear ordinary differential equations. These transformations generalise the Markovian systems obtained by Carverhill [8], Ritchken and Sankarasubramanian [20], Bhar and Chiarella [1], and Inui and Kijima [18], and also generalise the bond price formulae obtained therein.
Chiarella, C. & He, X.-.Z. 2000, 'Heterogeneous Beliefs, Risk and Learning in a Simple Asset Pricing Model with a Market Maker'.
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This paper attempts to study the dynamics of a simple discounted present value asset price model where agents have different risk attitudes and follow different expectation formulation schemes
for both first and second moments of the price distribution. Instead of using a Walrasian auctioneer scenario as the market clearing mechanism, a market maker scenario is used. In particular, the paper
concentrates on models of fundamentalists and trend traders who follow least squares learning processes. An analysis is made of the effects of lag lengths on the stability of the fundamental
equilibrium. Some necessary and/or sufficient conditions on the stability of the fundamental equilibrium associated with the speed of the adjustment of the market maker, different risk attitudes and
different risk attitudes and different values of lags (used in the learning process) are established. The results lead to the following observations: (I) Compared with the findings with the Walrasian
market clearing scenario in Brock and Hommes [8] and Chiarella and He [14], different price dynamics are obtained when the speed of the adjustment of the market maker increases and, in particular,
when the contrarians are involved in the model; (ii) In contrast to homogeneous beliefs, where the larger is the lag length the more stable is that in general (for both the Walrasian and the market maker
equilibrium) different lag lengths can complicate the price dynamics; (iii) In the model of trend followers versus contrarians, the stability of the fundamental equilibrium is determined by risk-adjusted
aggregated extrapolation rates. This indicates that although every individual forecasting rule may lead to divergence from the equilibrium, these may "cancel out" in the aggregate and the actual dynamics
with learning may thus be locally stable. On the other hand, only a small group of traders with expectation functions involving significant divergence can in fact destabilize the whole system.
Bhar, R. & Chiarella, C. 2000, 'Expectations in monetary policy in Australia implied by the probability distributions of interest rate derivatives', The European Journal of Finance, vol. 6, no. 2, pp. 113-125.
Chiarella, C. & Kwon, O.K. 2000, 'A complete Markovian stochastic volatility model in the HJM framework', Asia-Pacific Financial Markets, vol. 7, no. 4, pp. 293-304.
This paper considers a stochastic volatility version of the Heath, Jarrow and and Morton (1992) term structure model. Market completeness is obtained by adapting the Hobson and Rogers (1998) complete stochastic volatility stock market model to the interest rate setting. Numerical simulation for a special case is used to compare the stochastic volatility model against the traditional Vasicek (1977) model. © 2001 Kluwer Academic Publishers.
Chiarella, C., Flaschel, P. & Semmler, W. 2000, 'Price Flexibility and Debt Dynamics in a High Order AS-AD Model'.
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In this paper we reconsider extensions and modifications of earlier work on a disequilibrium model of AS-AD
growth. Our dynamic model exhibits more or less sluggishly adjusting prices and quantities, Keynesian demand rationing
and fluctuating capacity utilization for both labor and capital. Firms use debt (and pure profits) to finance their
investment expenditures. We first prove that the resulting 7D core dynamics are convergent (broadly speaking) for low
adjustment speeds. We then demonstrate partly analytically and partly numerically that their interior steady state will
lose asymptotic stability by way of Hopf bifurcations when relevant adjustment speeds are made sufficiently large. This
holds in particular for debt deflation, where falling price levels (caused by price flexibility that is sufficiently
high) cause significantly increasing real debt, falling investment and shrinking economic activity. This deepens the
deflationary process already under way. Such an instability result even occurs in the case where accompanying real wage
increases would support economic stability.
Chiarella, C. & Flaschel, P. 2000, 'High order disequilibrium growth dynamics: Theoretical aspects and numerical features', JOURNAL OF ECONOMIC DYNAMICS & CONTROL, vol. 24, no. 5-7, pp. 935-963.
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Bhar, R., Chiarella, C., El-Hassan, N. & Zheng, X. 2000, 'Reduction of forward rate dependent HJM models to Markovian form: pricing European bond options', Journal of Computational Finance, vol. 3, no. 3, pp. 47-72.
Chiarella, C. & Khomin, A. 1999, 'Adaptively evolving expectations in models of monetary dynamics: The fundamentalists forward looking', Annals of Operations Research, vol. 89, pp. 21-34.
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In the basic Cagan model of monetary dynamics, we allow inflationary expectations to be formed as a weighted average of fundamentalist and chartists expectations. We allow the weights to evolve adaptively according to the mechanism of Brock and Hommes [3] and study the resulting dynamic behaviour.
Chiarella, C., El-Hassan, N. & Kucera, A. 1999, 'Evaluation of American option prices in a path integral framework using Fourier-Hermite series expansions', Journal of Economic Dynamics and Control, vol. 23, no. 9-10, pp. 1387-1424.
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In this paper we review the path integral technique which has wide applications in statistical physics and relate it to the backward recursion technique which is widely used for the evaluation of derivative securities. We formulate the pricing of equity options, both European and American, using the path integral framework. Discretising in the time variable and using expansions in Fourier-Hermite series for the continuous representation of the underlying asset price, we show how these options can be evaluated in the path integral framework. For American options, the solution technique facilitates the accurate determination of the early exercise boundary as part of the solution. Additionally, the continuous representation of the state variable allows the relatively accurate and efficient evaluation of the option prices and the delta hedge ratio.
Chiarella, C. & Flaschel, P. 1999, 'Keynesian monetary growth dynamics in open economies', Annals of Operations Research, vol. 89, pp. 35-59.
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We investigate an open economy monetary growth model with sluggish price and quantity adjustments. It integrates the real dynamics of Rose's employment cycle, an inflationary dynamics of Cagan type, Metzlerian inventory dynamics and Dornbusch's exchange rate dynamics, implying eight laws of motion, two for each subdynamics. These intrinsically nonlinear 8D dynamics are asymptotically stable for low adjustment speeds of prices and expectations, give rise to Hopf bifurcations as these adjustment parameters are increased and lead to cyclically explosive behavior thereafter. Two extrinsic nonlinearities are therefore added, one in capital flows and the other a kinked Phillips curve. These two nonlinearities modify the dynamics radically, limiting them to economically meaningful domains even for extreme parameter choices.
Chiarella, C. & Flaschel, P. 1998, 'Dynamics of natural rates of growth and employment', MACROECONOMIC DYNAMICS, vol. 2, no. 3, pp. 345-368.
In this paper we consider how suppliers in a cobweb model may learn about their economic environment. Instead of assuming the one step backward-looking expectation scheme of the traditional linear cobweb model, we consider the subjective estimates of the statistical distribution of the market prices based on L-step backward time series of market clearing prices. With constant risk aversion, the cobweb model becomes nonlinear. Sufficient conditions on the local stability of the unique positive equilibrium of the nonlinear model are derived and, consequently, we show that the local stability region (of the parameters of the equation) is proportional to the lag length L When the equilibrium loses its local stability, we show that, for L=2, the model has strong 1:3 resonance bifurcation and a family of fixed points of order 3 becomes unstable on both sides of criticality. The numerical simulations suggest that the model has a simple global structure, it has no complicated dynamics as claimed recently by Boussard. However, complicated dynamics do appear when the model is modified with constant elasticity supply and demand.
Chiarella, C. & Vlacic, L. 1997, 'Preface to the special section on modelling and control of national and regional economies', CONTROL ENGINEERING PRACTICE, vol. 5, no. 4, pp. 517-518.
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Chiarella, C. & El-Hassan, N. 1997, 'Evaluation of Derivative Security Prices in the Heath-Jarrow-Morton Framework as Path Integrals Using Fast Fourier Transform Techniques'.
This paper considers the evaluation of derivative security prices within the Heath-Jarrow-Morton framework of
stochastic interest rates, such as bond options. Within this framework, the stochastic dynamics driving prices are in
general non-Markovian. Hence, in principle the partial differential equations governing prices require an infinite
dimensinal state space. We discuss a class of forward rate volatility functions which allow the stochastic dynamics to be
expressed in Markovian form and hence obtain a finite dimensional state space for the partial differential equations
governing prices. By applying to the Markovian form, the transformed suggested by Eydeland (1994), the pricing problem
can be set up as a path integral in function space. These integrals are evaluated using fast fourier transform techniques.
We apply the technique to the pricing of American bond options and compare the computational time with other methods
currently employed such as the method of lines and more traditional partial differential equation solution techniques.
Chiarella, C. & Khomin, A. 1996, 'An analysis of the complex dynamic behaviour of nonlinear oligopoly models with time delays', Chaos, Solitons and Fractals, vol. 7, no. 12, pp. 2049-2065.
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We consider the fate of output in the Cournot oligopoly model when the equilibrium is locally unstable. We discuss types of nonlinearities which may be present to bound the motion and introduce time lags in production and information which serve as bifurcation parameters. We apply the Hopf bifurcation theorem to determine conditions under which limit cycle motion is born, and use computer simulations to investigate the nature of the attractors generated by such models. Copyright © 1996 Elsevier Science Ltd.
Chiarella, C. 1996, 'Business cycles: Theory and empirical methods .8 - Semmler,W', JOURNAL OF ECONOMICS-ZEITSCHRIFT FUR NATIONALOKONOMIE, vol. 63, no. 2, pp. 224-227.
Chiarella, C. & Flaschel, P. 1996, 'Real and monetary cycles in models of Keynes-Wicksell type', JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION, vol. 30, no. 3, pp. 327-351.
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Chiarella, C. & Flaschel, P. 1996, 'An integrative approach to 2D-macromodels of growth, price and inventory dynamics', Chaos, Solitons and Fractals, vol. 7, no. 12, pp. 2105-2133.
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This paper investigates two variants of a Keynesian model of monetary growth with sluggish price and quantity adjustments. The first model integrates the real growth dynamics of Rose's employment cycle, an inflationary dynamics of the Cagan type and Metzler's inventory dynamics. This model is based on intrinsic nonlinearities solely and it implies for the private sector six laws of motion, two for each of the subdynamics stated above. It is shown that the integrated model does not at all preserve the insights obtained from the three prototype subdynamics. Since this model can give rise to global instabilities even for moderate adjustment speeds of prices and quantities, a variant of this model is then introduced which exhibits one fundamental 'nonintrinsic' nonlinearity in its wage adjustment mechanism. This nonlinearity makes the considered 6D-dynamics at the same time extremely 'viable' and complex, in particular for a high adjustment speed of nominal wages. Copyright © 1996 Elsevier Science Ltd.
Chiarella, C. & El-Hassan, N. 1996, 'A preference free partial differential equation for the term structure of interest rates', Asia-Pacific Financial Markets, vol. 3, no. 3, pp. 217-238.
The objectives of this paper are twofold: the first is the reconciliation of the differences between the Vasicek and the Heath-Jarrow-Morton approaches to the modelling of term structure of interest rates. We demonstrate that under certain (not empirically unreasonable) assumptions prices of interest-rate sensitive claims within the Heath-Jarrow-Morton framework can be expressed as a partial differential equation which both is preference-free and matches the currently observed yield curve. This partial differential equation is shown to be equivalent to the extended Vasicek model of Hull and White. The second is the pricing of interest rate claims in this framework. The preference free partial differential equation that we obtain has the added advantage that it allows us to bring to bear on the problem of evaluating American style contingent claims in a stochastic interest rate environment the various numerical techniques for solving free boundary value problems which have been developed in recent years such as the method of lines. © 1996 Kluwer Academic Publishers.
CHIARELLA, C. 1995, 'NONLINEAR DYNAMICS AND EVOLUTIONARY ECONOMICS - DAY,RH, CHEN,P', ECONOMIC RECORD, vol. 71, no. 214, pp. 303-305.
CHIARELLA, C. 1992, 'ECONOMIC-DYNAMICS - ZHANG,WB', JOURNAL OF ECONOMIC BEHAVIOR & ORGANIZATION, vol. 18, no. 3, pp. 443-445.
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Chiarella, C. 1991, 'The bifurcation of probability distributions in a non-linear rational expectations model of monetary economy', European Journal of Political Economy, vol. 7, no. 1, pp. 65-78.
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Much has been written about the stability of rational expectations models and in particular about the dynamic instability of a saddlepoint nature. The problem posed by this type of instability is usually solved by the jump-variable technique of allowing one of the endogenous variables to move discontinuously onto a stable manifold. The lack of an economic mechanism in these models to justify the use of such a procedure has remained a nagging problem in this literature. The present paper analyses the stability of a rational expectations models of a monetary economy by taking account of certain non-linearities in the money demand function imposed by budget constraints. A continuous time framework is used and the non-linear stochastic differential equation governing the dynamics is analysed via the corresponding Fokker-Planck equation. The continuous time framework allows us to show clearly that whilst the jump-variable technique may stabilise the mean of the time path of the economic variables, it can still leave the variance following an exploding time path. We find that the non-linear model exhibits stable behaviour without the imposition of any extraneous assumptions. It is also found that the probability distribution of the endogenous variables undergoes a bifurcation from a unimodal to a bimodal one. The latter distribution is characterised by the sharp changes in asset prices that are imposed arbitrarily in the traditional style of analysis. © 1991.
CHIARELLA, C., KEMP, M. & VANLONG, N. 1989, 'INNOVATION AND THE TRANSFER OF TECHNOLOGY - A LEADER-FOLLOWER MODEL', ECONOMIC MODELLING, vol. 6, no. 4, pp. 452-456.
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CHIARELLA, C. 1988, 'THE COBWEB MODEL - ITS INSTABILITY AND THE ONSET OF CHAOS', ECONOMIC MODELLING, vol. 5, no. 4, pp. 377-384.
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CHIARELLA, C. & SHANNON, A.G. 1986, 'AN EXAMPLE OF DIABETES COMPARTMENT MODELING', MATHEMATICAL MODELLING, vol. 7, no. 9-12, pp. 1239-1244.
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CHIARELLA, C. 1986, 'PERFECT FORESIGHT MODELS AND THE DYNAMIC INSTABILITY PROBLEM FROM A HIGHER VIEWPOINT', ECONOMIC MODELLING, vol. 3, no. 4, pp. 283-292.
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CHIARELLA, C., KEMP, M., VANLONG, N. & OKUGUCHI, K. 1984, 'ON THE ECONOMICS OF INTERNATIONAL FISHERIES', INTERNATIONAL ECONOMIC REVIEW, vol. 25, no. 1, pp. 85-92.
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CHIARELLA, C. & BOOKER, J. 1975, 'TIME-SETTLEMENT BEHAVIOR OF A RIGID DIE RESTING ON A DEEP CLAY LAYER', QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, vol. 28, no. AUG, pp. 317-328.
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CHIARELLA, C., CHARLTON, W. & ROBERTS, A. 1975, 'OPTIMUM CHUTE PROFILES IN GRAVITY FLOW OF GRANULAR MATERIALS - DISCRETE SEGMENT SOLUTION METHOD', JOURNAL OF ENGINEERING FOR INDUSTRY-TRANSACTIONS OF THE ASME, vol. 97, no. 1, pp. 10-13.
CHARLTON, W., CHIARELLA, C. & ROBERTS, A. 1975, 'GRAVITY FLOW OF GRANULAR MATERIALS IN CHUTES - OPTIMIZING FLOW PROPERTIES', JOURNAL OF AGRICULTURAL ENGINEERING RESEARCH, vol. 20, no. 1, pp. 39-45.
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Other
Chiarella, C., He, X.-.Z., Shi, L. & Wei, L. 2014, 'A Behavioural Model of Investor Sentiment in Limit Order Markets'.
This paper examines the effect of behavioral sentiment in a limit order market when agents are risk averse and arrive in the market with different time horizons. The order submission rules with respect to order type and size
are determined by maximizing the expected utility of agents with heterogeneous beliefs on the fundamental price and investment horizon. We show that behavioral sentiment has a double-edge impact on market quality: it improves market
liquidity by reducing bid-ask spread and market volatility but increasing trading volume; however, it reduces pricing ef?ciency by increasing the price deviation from the fundamental value. Consistent with empirical observations, the
model is able to replicate a number of stylized facts and limit book phenomena, including insigni?cant autocorrelations in returns, but signi?cant and decaying autocorrelations in the absolute returns, the bid-ask spread and the
trading volume, hump shaped order books, a concave relationship between trade imbalance and average mid-price returns, and event clustering in order submissions. More important, the behavioral sentiment plays a very important role in
explaining the positive autocorrelation in trading volume and also event clustering.
Cheang, G.H.L., Chiarella, C. & Ziogas, A. 2013, 'The representation of American options prices under stochastic volatility and jump-diffusion dynamics'.
Adolfsson, T., Chiarella, C., Ziogas, A. & Ziveyi, J. 2013, 'Representation and Numerical Approximation of American Option Prices under Heston Stochastic Volatility Dynamics'.
In this paper we consider the evaluation of American call options on dividend paying stocks in the case where the underlying asset price evolves according to Heston's (1993) stochastic volatility model. We solve the
Kolmogorov partial differential equation associated with the driving stochastic processes using a combination of Fourier and Laplace transforms and so obtain the joint transition probability density function for the underlying
processes. We then use Duhamel's principle to obtain the expression for the American option price, which depends upon the unknown early exercise surface. By evaluating the pricing equation along the free surface boundary, we
obtain the corresponding integral equation for the early exercise surface. An algorithm is proposed for solving the integral equation system, based upon numerical integration techniques for Volterra integral equations. The method is
used to explore the impact of stochastic volatility on the price and free boundary of American call options.
Chiarella, C. & Guilmi, C.D. 2013, 'Monetary Policy and Debt Deflation: Some Computational Experiments'.
The paper presents an agent based model to study the possible effects of different fiscal and monetary policies in the context of debt deflation. We introduce a modified Taylor rule which includes the financial position of
firms as a target. Monte Carlo simulations show that an excessive sensitivity of the central bank to inflation, the output gap and firms' debt can have undesired and destabilising effects on the system, while an active fiscal policy
appears to be able to effectively stabilise the economy. The paper also addresses the puzzle of low inflation during stock market booms by testing different behavioural rules for the central bank. We find that, in a context of sticky
prices and volatile expectations, endogenous credit can be identified as the main source of the divergent dynamics of prices in the real and financial sector.
Chiarella, C., Griebsch, S. & Kang, B. 2013, 'Investigating Time-Efficient Methods to Price Compound Options in the Heston Model'.
The primary purpose of this paper is to provide an in-depth analysis of a number of structurally different methods to numerically evaluate European compound option prices under Heston's stochastic volatility dynamics.
Therefore, we first outline several approaches that can be used to price these type of options in the Heston model: a modified sparse grid method, a fractional fast Fourier transform technique, a (semi-)analytical valuation formula
using the Green's function of logarithmic spot and volatility and a Monte Carlo simulation. Then we compare the methods on a theoretical basis and report on their numerical properties with respect to computational times and accuracy.
One key element of our analysis is that the analyzed methods are extended to incorporate piecewise time-dependent model parameters, which allows for a more realistic compound option pricing.
Chiarella, C., He, X.-.Z. & Pellizzari, P. 2012, 'A DYNAMIC ANALYSIS OF THE MICROSTRUCTURE OF MOVING AVERAGE RULES IN A DOUBLE AUCTION MARKET'.
Beyna, I., Chiarella, C. & Kang, B. 2012, 'Pricing Interest Rate Derivatives in a Multifactor HJM Model with Time'.
We investigate the partial differential equation (PDE) for pricing interest derivatives in the multi-factor Cheyette Model, which involves time-dependent volatility functions with a special structure. The high dimensional
parabolic PDE that results is solved numerically via a modified sparse grid approach, that turns out to be accurate and efficient. In addition we study the corresponding Monte Carlo simulation, which is fast since the distribution of
the state variables can be calculated explicitly. The results obtained from both methodologies are compared to the known analytical solutions for bonds and caplets. When there is no analytical solution, both European and Bermudan
swaptions have been evaluated using the sparse grid PDE approach that is shown to outperform the Monte Carlo simulation.
Chiarella, C., Lo, C.-.F. & Huang, M.X. 2012, 'Modelling Default Correlations in a Two-Firm Model with Dynamic Leverage Ratios'.
This article provides a generalized two-firm model of default correlation, based on the structural approach that incorporates interest rate risk. In most structural models default is driven by the
firms' asset dynamics. In this article, a two-firm model of default is instead driven by the dynamic leverage ratios, which combines the measure of risks of the firms' total liabilities and assets. This
article investigates analytical methods and numerical tools to solve the two-dimensional first passage time problem with time-dependent parameters. We carry out a comparative analysis of the impact of
model parameters and provide some insights of their effects on joint survival probabilities and default correlations.
Chiarella, C., Fanelli, V. & Musti, S. 2011, 'Modelling the evolution of credit spreads using the Cox process within the HJM framework: A CDS option pricing model'.
In this paper a simulation approach for defaultable yield curves is developed within the Heath et al. (1992) framework. The default event is modelled using the Cox process where the stochastic intensity represents the credit spread. The forward credit spread volatility function is affected by the entire credit spread term structure. The paper provides the defaultable bond and credit default swap option price in a probability setting equipped with a subfiltration structure. The Euler-Maruyama stochastic integral approximation and the Monte Carlo method are applied to develop a numerical scheme for pricing. Finally, the antithetic variable technique is used to reduce the variance of credit default swap option prices. © 2010 Elsevier B.V. All rights reserved.
Cheang, G. & Chiarella, C. 2011, 'A Modern View on Merton's Jump-Diffusion Model'.
Merton has provided a formula for the price of a European call option on a single stock where the stock price process contains a continuous Poisson jump component, in addition to a continuous
log-normally distributed component. In Merton's analysis, the jump-risk is not priced. Thus the distribution of the jump-arrivals and the jump-sizes do not change under the change of measure. We go onto
introduce a Radon-Nikodym derivative process that induces the change of measure from the market measure to an equivalent martingale measure. The choice of parameters in the Radon-Nikodym derivative
allows us to price the option under different financial-economic scenarios. We introduce a hedging argument that eliminates the jump-risk in some sort of averaged sense, and derive an integro-partial
differential equation of the option price that is related to the one obtained by Merton.
Chiarella, C. & Ziveyi, J. 2011, 'Two Stochastic Volatility Processes - American Option Pricing'.
In this paper we consider the pricing of an American call option whose underlying asset dynamics evolve under the influence of two independent stochastic volatility processes of the Heston (1993)
type. We derive the associated partial differential equation (PDE) of the option price using hedging arguments and Ito's lemma. An integral expression for the general solution of the PDE is presented by
using Duhamel's principle and this is expressed in terms of the joint transition density function for the driving stochastic processes. We solve the Kolmogorov PDE for the joint transition density function
by first transforming it to a corresponding system of characteristic PDEs using a combination of Fourier and Laplace transforms. The characteristic PDE system is solved by using the method of
characteristics. With the full price representation in place, numerical results are presented by first approximating the early exercise surface with a bivariate log linear function. We perform numerical
comparisons with results generated by the method of lines algorithm and note that our approach is very competitive in terms of accuracy.
Chiarella, C., Clewlow, L. & Kang, B. 2011, 'The Evaluation of Multiple Year Gas Sales Agreement with Regime Switching'.
A typical gas sales agreement (GSA) also called a gas swing contract, is an agreement between a supplier and a purchaser for the delivery of variable daily quantities of gas, between specified
minimum and maximum daily limits, over a certain number of years at a specified set of contract prices. The main constraint of such an agreement that makes them difficult to value are that in each gas year
there is a minimum volume of gas (termed take-or-pay or minimum bill) for which the buyer will be charged at the end of the year (or penalty date), regardless of the actual quantity of gas taken. We
propose a framework for pricing such swing contracts for an underlying gas forward price curve that follows a regime-switching process in order to better capture the volatility behaviour in such markets.
With the help of a recombing pentanonial tree, we are able to efficiently evaluate the prices of the swing contracts, find optimal daily decisions and optimaly early use of both the make-up bank and the
carry forward bank at different regimes. We also show how the change of regime will affect the decisions.
Chiarella, C., Kang, B. & Meyer, G. 2010, 'The evaluation of barrier option prices under stochastic volatility', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 266 Abstract: This paperc onsiders the problem o fnumerically evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Heston (1993). We develop a method of lines approach to evaluate the price as well as the delta and gamma of the option. The method is able to effciently handle bothc ontinuously monitored and discretely monitored barrier options and can also handle barrier options with early exercise features. In the latter case, we can calculate the early exercise boundary of an American barrier option in both the continuously and discretely monitored cases.
Chiarella, C., Hung, H. & Flaschel, P. 2010, 'Keynesian disequilibrium dynamics: Estimated convergence, roads to instability and the emergence of complex business fluctuations', QFRC Research Paper.
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We reformulate the traditional AS-AD growth model of the Neoclassical Synthesis (stage I) with a Taylor policy rule replacing the conventional LM-curve, with gradually adjusting wages as well as prices, and with perfect foresight on current inflation rates and an adaptively revised notion of an inflationary climate in which the economy is operating. We compare this approach with the New Keynesian approach, the Neoclassical Synthesis, stage II, with staggered price and wage setting and find various common components, yet with radically different dynamic implications due to our treatment of the forward-looking part of our wage-price spiral. We show for a system estimate of our model that it implies qualitatively local asymptotic stability and when its estimated form is simulated in response to isolated shocks strongly damped business fluctuations, due to a stable interaction of goods market dynamics with the interest rate policy of the central bank and due to a normal working of a real-wage feedback chain. These results are however endangered â leading in fact to economic breakdown â when there is a global floor to money wage inflation rates. In this case, the return of some money wage flexibility in deep depressions is of help in restoring viability of the model, thereby even avoiding explosive dynamics and the collapse of the economy. This situation leads to viable, but complex business fluctuations
Chiarella, C., Maina, S.C. & Nikitopoulos-Sklibosios, C. 2010, 'Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility'.
This paper presents a class of defaultable term structure models within the HJM framework with stochastic volatility. Under certain volatility specifications, the model admits finite dimensional
Markovian structures and consequently provides tractable solutions for interest rate derivatives. We also investigate the effect of stochastic volatility and of correlation between the stochastic
volatility and credit spreads on the defaultable short rate and defaultable bond prices.
Chiarella, C. & Hsiao, C.-.Y. 2010, 'Optimal Investment Strategies under Stochastic Volatility - Estimation and Applications'.
This paper studies the impact of stochastic volatility (SV) on optimal investment decisions. We consider three different SV models: an extended Stein/Stein model, the Heston Model and an extended
Heston Model with a constant elasticity variance (CEV) process and derive the the long-term optimal investment strategies under each of these processes. Since volatility is not a directly observable
quantity, extended Kalman filter techniques are adopted to deal with this partial information problem. Optimal investment strategies based on the CEV volatility model are obtained by adopting the Backward
Markov Chain approximation method since analytical solutions are no longer available. We find in the empirical investigation that the Heston model is favored as a more parsimonious model compared with the
other two models. All three investment strategies based on the three SV models contain a positive intertemporal hedging term in addition to the static mean-variance portfolio. However, in their details the
three investment strategies differ from each other. We also ?nd that the investment strategies are sensitive to the CEV parameter.
Chiarella, C., Hsiao, C.-.Y. & Huang, M.X. 2010, 'A Survey of Non-linear Methods for No-arbitrage Bond Pricing'.
Chiarella, C., Iori, G. & Perelló, J. 2009, 'The impact of heterogeneous trading rules on the limit order book and order flows'.
In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules. Agents are assumed to have three components of the expectation of future asset returns, namely fundamentalist, chartist and noise trader. Furthermore agents differ in the characteristics describing these components, such as time horizon, risk aversion and the weights given to the various components. The model developed here extends a great deal of earlier literature in that the order submissions of agents are determined by utility maximisation, rather than the mechanical unit order size that is commonly assumed. In this way the order flow is better related to the ongoing evolution of the market. For the given market structure we analyze the impact of the three components of the trading strategies on the statistical properties of prices and order flows and observe that it is the chartist strategy that is mainly responsible of the fat tails and clustering in the artificial price data generated by the model. The paper provides further evidence that large price changes are likely to be generated by the presence of large gaps in the book. © 2008 Elsevier B.V. All rights reserved.
Chiarella, C., Dieci, R. & He, X.-.Z. 2009, 'Heterogeneity, Market Mechanisms, and Asset Price Dynamics', Handbook of Financial Markets: Dynamics and Evolution.
Although there might be agreement that the standard paradigm does not fully explain what is causing the evolution of speculative asset prices, there may be less agreement on where to start to build an improved paradigm. By and large, the view that has been adopted in the boundedly rational heterogeneous agent literature is to retain expected utility maximization as the goal of each agent but to allow the agents to have different risk preferences and different expectations, rather than the single homogeneous rational expectation, about future possible returns. The expectations differ since agents are assumed to have different information and beliefs. Thus the asset price modeling framework is based on the fact that trading is driven more by differences in expectations than by the random arrival of news events. Within this framework, a simple market of one risky asset and one risk-free asset, with agents having different expectations, is considered with two different types of utility functions and two different market-clearing mechanisms. The framework provides the basic elements and structure of the various models. The basic building blocks of this framework are portfolio optimization, agents' utility functions, the market-clearing mechanism, and expectations feedback. © 2009 Elsevier Inc. All rights reserved.
Chiarella, C., He, X. & Zheng, M. 2009, 'Heterogeneous Expectations and Exchange Rate Dynamics (243)', Quantitative Finance Research Paper Series.
This paper presents a continuous-time model of exchange rates relying not only on macroeconomic factors but also having a market microstructure component. The driving macroeconomic factor is the interest rate differential, while the market microstructure element is described by the expectations of boundedly rational portfolio managers who use a weighted average of the expectations of fundamentalists and chartists. Within this framework, the different roles of the macroeconomic factors and market microstructure elements on the determination of the exchange rate are examined explicitly. We show that this simple model generates very complicated market behaviour, including the existence of multiple steady state equilibria, the deviations of the market exchange rate from the fundamental, and market fluctuations. Numerical simulation of the corresponding stochastic version of the model shows that the model is able to generate typical time series and volatility clustering patterns observed in exchange rate markets.
Chiarella, C. & Kang, B. 2009, 'The Evaluation of American Compound Option Prices Under Stochastic Volatility Using the Sparse Grid Approach (245)', Quantitative Finance Research Paper Series.
A compound option (the mother option) gives the holder the right, but not obligation to buy (long) or sell (short) the underlying option (the daughter option). In this paper, we demonstrate a partial differential equation (PDE) approach to pricing American-type compound options where the underlying dynamics follow Hestonâs stochastic volatility model. This price is formulated as the solution to a two-pass free boundary PDE problem. A modified sparse grid approach is implemented to solve the PDEs, which is shown to be accurate and efficient compared with the results from Monte Carlo simulation combined with the Method of Lines.
CHIARELLA, C.A.R.L., KANG, B.O.D.A., MEYER, G.U.N.T.E.R.H. & ZIOGAS, A.N.D.R.E.W. 2009, 'THE EVALUATION OF AMERICAN OPTION PRICES UNDER STOCHASTIC VOLATILITY AND JUMP-DIFFUSION DYNAMICS USING THE METHOD OF LINES'.
This paper considers the problem of numerically evaluating American option prices when the dynamics of the underlying are driven by both stochastic volatility following the square root process of Heston [18], and by a Poisson jump process of the type originally introduced by Merton [25]. We develop a method of lines algorithm to evaluate the price as well as the delta and gamma of the option, thereby extending the method developed by Meyer [26] for the case of jump-diffusion dynamics. The accuracy of the method is tested against two numerical methods that directly solve the integro-partial differential pricing equation. The first is an extension to the jump-diffusion situation of the componentwise splitting method of Ikonen and Toivanen [21]. The second method is a Crank-Nicolson scheme that is solved using projected successive over relaxation and which is taken as the benchmark for the price. The relative efficiency of these methods for computing the American call option price, delta, gamma and free boundary is analysed. If one seeks an algorithm that gives not only the price but also the delta and gamma to the same level of accuracy for a given computational effort then the method of lines seems to perform best amongst the methods considered.
Chiarella, C., Clewlow, L. & Kang, B. 2009, 'Modelling and estimating the forward price curve in the energy market', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 260 Abstract: The stochastic or random nature of commodity prices plays a central role in models for valuing ?nancial contingent claims on commodities. In this paper, by enhancing a multifactor framework which is consistent not only with the market observable forward price curve but also the volatilities and correlations of forward prices, we propose a two factor stochastic volatility model for the evolution of the gas forward curve. The volatility is stochastic due to a hidden Markov Chain that causes it to switch between âon peakâ? and âoff peakâ? states. Based on the structure functional forms for the volatility, we propose and implement the Markov Chain Monte Carlo (MCMC) method to estimate the parameters of the forward curve model. Applications to simulated data indicate that the proposed algorithm is able to accommodate more general features, such as regimes witching and seasonality. Applications to the market gas forward data shows that the MCMC approach provides stable estimates.
Chiarella, C., Dieci, R. & He, X. 2009, 'A framework for CAPM with heterogenous beliefs', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 254 Abstract: We introduce heterogeneous beliefs in to the mean-variance framework of the standard CAPM, in contrast to the standard approach which assumes homogeneous beliefs. By assuming that agents form optimal portfolios based upon their heterogeneous beliefs about conditional means and covariances of the risky asset returns, we set up a framework for the CAPM that incorporates the heterogeneous beliefs when the market is in equilibrium. In this framework we first construct a consensus belief (with respect to the means and covariances of the risky asset returns) to represent the aggregate market belief when the market is in equilibrium. We then extend the analysis to a repeated one-period set-up and establish a framework for a dynamic CAPM using a market fraction model in which agents are grouped according to their beliefs. The exact relation between heterogeneous beliefs, the market equilibrium returns and the ex-ante beta-coeffcients is obtained. CAPM and Heterogeneous beliefs.
Cheang, G., Chiarella, C. & Ziogas, A. 2009, 'An Analysis of American Options under Heston Stochastic Volatility and Jump-Diffusion Dynamics'.
This paper considers the problem of pricing American options when the dynamics of the underlying are driven by both stochastic volatility following a square root process as used by Heston (1993),
and by a Poisson jump process as introduced by Merton (1976). Probability arguments are invoked to find a representation of the solution in terms of expectations over the joint distribution of the underlying
process. A combination of Fourier transform in the log stock price and Laplace transform in the volatility is then applied to find the transition probability density function of the underlying process. It
turns out that the price is given by an integral dependent upon the early exercise surface, for which a corresponding integral equation is obtained. The solution generalises in an intuitive way the
structure of the solution to the corresponding European option pricing problem in the case of a call option and constant interest rates obtained by Scott (1997).
Cheang, G.H.L. & Chiarella, C. 2008, 'Hedge Portfolios in Markets with Price Discontinuities'.
We consider a market consisting of multiple assets under jump-diffusion dynamics with European style options written on these assets. It is well-known that such markets are incomplete in the
Harrison and Pliska sense. We derive a pricing relation by adopting a Radon-Nikodym derivative based on the exponential martingale of a correlated Brownian motion process and a multivariate compound
Poisson process. The parameters in the Radon-Nikodym derivative define a family of equivalent martingale measures in the model, and we derive the corresponding integro-partial differential equation for
the option price. We also derive the pricing relation by setting up a hedge portfolio containing an appropriate number of options to "complete" the market. The market prices of jump-risks are priced in
the hedge portfolio and we relate these to the choice of the parameters in the Radon-Nikodym derivative used in the alternative derivation of the integro-partial differential equation.
Cheang, G.H.L. & Chiarella, C. 2008, 'Exchange Options Under Jump-Diffusion Dynamics'.
Margrabe provides a pricing formula for an exchange option where the distributions of both stock prices are log-normal with correlated Wiener components. Merton has provided a formula for the
price of a European call option on a single stock where the stock price process contains a continuous Poisson jump component, in addition to a continuous log-normally distributed component. We use
Merton's analysis to extend Margrabe's results to the case of exchange options where both stock price processes also contain compound Poisson jump components. A Radon-Nikod´ym derivative process that
induces the change of measure from the market measure to an equivalent martingale measure is introduced. The choice of parameters in the Radon-Nikod´ym derivative allows us to price the option under
different financial-economic scenarios. We also consider American style exchange options and provide a probabilistic intepretation of the early exercise premium.
Chiarella, C., Dieci, R. & He, X.-.Z. 2007, 'Heterogeneous expectations and speculative behavior in a dynamic multi-asset framework'.
Chiarella, C., He, X. & Zheng, M. 2007, 'The Stochastic Dynamics of Speculative Prices (208)', Quantitative Finance Research Paper Series.
Within the framework of the heterogeneous agent paradigm, we establish a stochastic model of speculative price dynamics involving of two types of agents, fundamentalists and chartists, and the market price equilibria of which can be characterised by the invariant measures of a random dynamical system. By conducting a stochastic bifurcation analysis, we examine the market impact of speculative behaviour. We show that, when the chartists use lagged price trends to form their expectations, the market equilibrium price can be characterised by a unique and stable invariant measure when the activity of the speculators is below a certain critical value. If this threshold is surpassed, the market equilibrium can be characterised by more than two invariant measures, of which one is completely stable, another is completely unstable and the remaining ones may exhibit various types of stability. Also, the corresponding stationary measure displays a significant qualitative change near the threshold value. We show that the stochastic model displays behaviour consistent with that of the underlying deterministic model. However, when the time lag in the formation of the price trends used by the chartists approaches zero, such consistency breaks down. In addition, the change in the stationary distribution is consistent with a number of market anomalies and stylised facts observed in financial markets, including a bimodal logarithmic price distribution and fat tails.
Chiarella, C., Hsiao, C.-.Y. & Semmler, W. 2007, 'Intertemporal Investment Strategies under Inflation Risk'.
This paper studies intertemporal investment strategies under inflation risk by extending the intertemporal framework of Merton (1973) to include a stochastic price index. The stochastic price
index gives rise to a two-tier evaluation system: agents maximize their utility of consumption in real terms while investment activities and wealth evolution are evaluated in nominal terms. We include
inflation-indexed bonds in the agents' investment opportunity set and study their effectiveness in hedging against inflation risk. A new multifactor term structure model is developed to price both
inflation-indexed bonds and nominal bonds, and the optimal rules for intertemporal portfolio allocation, both with and without inflation-indexed bonds are obtained in closed form. The theoretical model is
estimated using data of US bond yield, both real and nominal, and S&P 500 index. The estimation results are employed to construct the optimal investment strategy for an actual real market situation.
Wachter (2003) pointed out that without inflation risk, the most risk averse agents (with an infinite risk aversion parameter) will invest all their wealth in the long term nominal bond maturing at the
end of the investment horizon. We extend this result to the case with inflation risk and conclude that the most risk averse agents will now invest all their wealth in the inflation-indexed bond maturing
at the end of the investment horizon.
Chiarella, C. & Platen, E. 2007, 'The History of the Quantitative Methods in Finance Conference Series. 1992-2007'.
This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who
presented at all 15 conferences and the titles of their papers.
Asada, T., Chiarella, C., Flaschel, P. & Proaño, C.R. 2007, 'Keynesian AD-AS, Quo Vadis?'.
We formulate a dynamic AD-AS model based on gradually adjusting wages and prices, perfect foresight of current inflation rates
and adaptive expectations concerning the inflation climate in which the economy operates. The model consists of a wage and a price
Phillips curve, a dynamic IS curve as well as a dynamic employment adjustment equation (Okun's law) and a Taylor interest rate rule. The
model can be reduced to a 3D dynamical system by a suitable choice of the Taylor rule and implies strong stability results, in particular
for an appropriately chosen interest rate policy rule. Through instrumental variables GMM system estimation with aggregate time series
data for the U.K. economy, we obtain parameter estimates which support the specification of our theoretical model and its stability
implications. We contrast these results with the standard (formally similarly structured) New Keynesian model with staggered wage and
price setting where determinacy of the dynamics represents a severe problem and where (if determinacy can be achieved) inertia-free
stability is obtained by the very choice of the solution method.
Chiarella, C., Dieci, R. & Gardini, L. 2006, 'Asset price and wealth dynamics in a financial market with heterogeneous agents'.
Chiarella, C. & He, X. 2006, 'Aggregation of heterogeneous beliefs and asset pricing theory: A mean-variance analysis', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Paper Number: 186
Chiarella, C. & Ziogas, A. 2006, 'American Call Options on Jump-Diffusion Processes: A Fourier Transform Approach'.
This paper considers the Fourier transform approach to derive the implicit integral equation for the price of an American call option in the case where the underlying asset follows a
jump-diffusion process. Using the method of Jamshidian (1992), we demonstrate that the call option price is given by the solution to an inhomogeneous integro-partial differential equation in an unbounded
domain, and subsequently derive the solution using Fourier transforms. We also extend McKean's incomplete Fourier transform approach to solve the free boundary problem under Merton's framework, for a
general jump size distribution. We show how the two methods are related to each other, and also to the Geske-Johnson compound option approach used by Gukhal (2001). The paper also derives results
concerning the limit for the free boundary at expiry, and presents a numerical algorithm for solving the linked integral equation system for the American call price, delta and early exercise boundary.
This scheme is applied to Merton's jump-diffusion model, where the jumps are log-normally distributed.
Rothig, A. & Chiarella, C. 2006, 'Investigating nonlinear speculation in cattle, corn and hog futures markets using logistic smooth transition regression models', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 172 Abstract: This article explores nonlinearities in the response of speculatorsâ trading activity to price changes in live cattle, corn, and lean hog futures markets. Analyzing weekly data from March 4, 1997 to December 27, 2005, we reject linearity in all of these markets. Using smooth transition regression models, we find a similar structure of nonlinearities with regard to the number of different regimes, the choice of the transition variable, and the value at which the transition occurs.
Chiarella, C., Hung, H. & To, T. 2005, 'The volatility structure of the fixed income market under the HJM framework: a non-linear filtering approach (QFRC paper #151)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp151.pdf
Chiarella, C., Nikitopoulos-Sklibosios, C. & Schlogl, E. 2005, 'A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton with Jumps'.
This paper examines the pricing of interest rate derivatives when the interest rate dynamics experience infrequent jump shocks modelled as a Poisson process and within the Markovian HJM framework
developed in Chiarella & Nikitopoulos (2003). Closed form solutions for the price of a bond option under deterministic volatility specifications are derived and a control variate numerical method is
developed under a more general state dependent volatility structure, a case in which closed form solutions are generally not possible. In doing so, we provide a novel perspective on the control variate
methods by going outside a given complex model to a simpler more tractable setting to provide the control variates.
Chiarella, C. & To, T. 2005, 'The multifactor nature of the volatility of the Eurodollar futures market (QFRC paper #150)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp150.pdf
Chiarella, C. & Ziogas, A. 2005, 'Pricing American options on jump-diffusion processes using Fourier Hermite series expansions (QFRC paper #145)'.
ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp145.pdf
Chiarella, C. & Hsiao, C. 2005, 'The impact of short-sale constraints on asset allocation strategies via the backward Markov chain approximation method', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 171 Abstract: This paper considers an asset allocation strategy over a finite period under investment uncertainty and short-sale constraints as a continuous time stochastic control problem. Investment uncertainty is characterised by a stochastic interest rate and inflation risk. If there are no short-sale constraints, the optimal asset allocation strategy can be solved analytically. We consider several kinds of short-sale constraints and employ the backward Markov chain approximation method to explore the impact of short-sale constraints on asset allocation decisions. Our results show that the short-sale constraints do indeed have a significant impact on the asset allocation decisions.
Chiarella, C., He, T. & Hommes, C.H. 2005, 'A Dynamic Analysis of Moving Average Rules'.
The use of various moving average (MA) rules remains popular with financial market practitioners. These rules have recently become the focus of a number empirical studies, but there have been very few studies of financial market models where some agents employ technical trading rules of the type used in practice. In this paper we propose a dynamic financial market model in which demand for traded assets has both a fundamentalist and a chartist component. The chartist demand is governed by the difference between current price and a (long-run) MA. Both types of traders are boundedly rational in the sense that, based on a fitness measure such as realized capital gains, traders switch from a strategy with low fitness to the one with high fitness. We characterize the stability and bifurcation properties of the underlying deterministic model via the reaction coefficient of the fundamentalists, the extrapolation rate of the chartists and the lag length used for the MA. By increasing the intensity of choice to switching strategies, we then examine various rational routes to randomness for different MA rules. The price dynamics of the moving average rule are also examined and one of our main findings is that an increase of the window length of the MA rule can destabilize an otherwise stable system, leading to more complicated, even chaotic behaviour. The analysis of the corresponding stochastic model is able to explain various market price phenomena, including temporary bubbles, sudden market crashes, price resistance and price switching between different levels.
Asada, T., Chen, P., Chiarella, C. & Flaschel, P. 2004, 'Keynesian dynamics and the wage price spiral: a baseline disequilibrium approach (Centre for Empirical Macroeconomics, University of Bielefeld, paper #69)'.
Bhar, R., Chiarella, C., Hung, H. & Runggaldier, W.J. 2004, 'The volatility of the instantaneous spot interest rate implied by arbitrage pricing - a dynamic Bayesian approach (School of Banking & Finance, UNSW, paper #2004-6)'.
Bhar, R., Chiarella, C. & To, T. 2004, 'Estimating the volatility structure of an arbitrage-free interest rate model via the futures markets (School of Banking & Finance, UNSW, paper #2004-5)'.
Chiarella, C., El-Hassan, N. & Kucera, A. 2004, 'Evaluation of Point Barrier Options in a Path Integral Framework Using Fourier-Hermite Expansions'.
The pricing of point barrier or discretely monitored barrier options is a difficult problem. In general, there is no known closed form solution for pricing such options. In this paper we develop
a path integral approach to the evaluation of barrier options. This leads to a backward recursion functional equation linking the pricing functions at successive barrier points. We solve this functional
equation by expanding the pricing functions in Fourier-Hermite series. The backward recursion functional equation then becomes the backward recurrence relation for the coefficients in the Fourier-Hermite
expansion of the pricing functions. We thus obtain a very efficient and accurate method for generating the pricing function at any barrier point. We perform a number of numerical experiments with the
method in order to gain some understanding of the nature of convergence. We present results for various volatility values and different numbers of basis functions in the Fourier-Hermite expansion.
Comparisons will be given between pricing of point barriers in the path integral framework and by use of finite difference methods.
Chiarella, C., He, X. & Hommes, C. 2004, 'A dynamic analysis of moving average rules (QFRC paper #133)'.
Chiarella, C., Kucera, A. & Ziogas, A. 2004, 'A survey of the integral representation of American option prices (QFRC paper #118)'.
Chiarella, C. & Ziogas, A. 2004, 'Mckean's methods applied to American option prices (QFRC paper #117)'.
Hsiao, C., Chiarella, C. & Semmler, W. 2004, 'Strategic asset allocation with arbitrage-free bond market using dynamic programing (Centre for Empirical MacroEconomics, University of Bielefeld, paper #76)'.
Chiarella, C., He, X. & Hommes, C. 2004, 'A dynamic analysis of moving average rules (Centre for Nonlinear Dynamics in Economics & Finance, University of Amsterdam, paper #04-14)', 10th International conference on computing in economics and finance.
Chiarella, C., He, X. & Wang, D. 2004, 'Statistical Properties of a Heterogeneous Asset Price Model with Time-Varying Second Moment', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 142 Abstract: Stability and bifurcation analysis of deterministic systems has been widely used in modeling financial markets. However, the impact of such dynamic phenomena on various statistical properties of the corresponding stochastic model, including skewness and excess kurtosis, various autocorrelation (AC) patterns of under and over reactions, and volatility clustering characterised by the long-range dependence of ACs, is not clear and has been very little studied. This paper aims to study this issue. Through a simple behavioural asset pricing model with fundamentalists and chartists, we examine the statistical properties of the model and their connection to the dynamics of the underlying deterministic model. In particular, our analysis leads to some insights into the type of mechanism that may be generating some of the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data.
Chiarella, C., He, X. & Wang, D. 2004, 'A behavioural asset pricing model with a time-varying second moment', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 141 Abstract: We develop a simple behavioural asset pricing model with fundamentalists and chartists to study price behaviour in financial markets. Within our model, the market impact of the weighting process of the conditional mean and variance of the chartists and investors' reactions are analysed. Price dynamics of the deterministic model under/over-reactions are analyzed. It shows different price dynamics and routes to complicated price behaviour when the chartists act as either trend followers or contrarians. It is found that (in a separate paper Chiarella et al (2004)) this analysis can be used to establish some connections between the statistical properties of the nonlinear stochastic system (such as distribution density and autocorrelation patterns of returns, in particular the stylised facts, such as fat tails, skewness, high kurtosis and long memory, observed in high frequency financial data) and the stability and bifurcation of the underlying deterministic system are established.
Chiarella, C., Kucera, A. & Ziogas, A. 2004, 'A Survey of the Integral Representation of American Option Prices'.
This paper surveys some of the literature on American option pricing, in particular the representations of McKean (1965), Kim (1990) and Carr, Jarrow and Myneni (1992). It is proposed that the
approach regarding the problem as a free boundary value problem, and solving this via incomplete Fourier transforms, is the most robust for further developments involving more complex payo structures,
and higher dimensional problems such as multi-asset American options. Some comparison of di erent numerical solution methods is also provided.
Chiarella, C. & Gao, S. 2004, 'Continuous Time Model Estimation'.
This paper introduces an easy to follow method for continuous time model estimation. It serves as an introduction
on how to convert a state space model from continuous time to discrete time, how to decompose a hybrid stochastic model
into a trend model plus a noise model, how to estimate the trend model by simulation, and how to calculate standard errors
from estimation of the noise model. It also discusses the numerical difficulties involved in discrete time models that
bring about the unit roots illusion in econometrics.
Bhar, R., Chiarella, C. & To, T.-.D. 2004, 'Estimating the Volatility Structure of an Arbitrage-Free Interest Rate Model Via the Futures Markets'.
This paper considers a class of Heath-Jarrow-Morton (1992) term
structure models, characterized by time deterministic volatilities for
the instantaneous forward rate. The bias that arises from using observed
futures yields as a proxy for the unobserved instantaneous forward rate
is analyzed. The fact that futures contracts can be viewed as derivative
instruments on the forward rate is used to determine the likelihood
function for futures prices. The likelihood transformation method of
Duan (1994) is then used to obtain the full information maximum
likelihood estimator for the observable futures prices. The approach is
applied to estimate the volatility structure implied by futures
contracts traded on the Chicago Mercantile Exchange.
Asada, T., Chiarella, C. & Flaschel, P. 2003, 'Keynes-Metzler-Goodwin Model Building: The Closed Economy'.
In the framework of a recently established Keynesian type monetary macro model, the so-called KMG model, we
study implications of kinked Phillips curves and alternative monetary policy rules. As alternative monetary policy
rules we consider monetary growth targeting and interest rate targeting (the Taylor rule). Our monetary macro model
exhibits: asset market clearing, disequilibrium in product and labor markets, sluggish price and quantity adjustments,
two Phillips-Curves for wage and price dynamics, and a combination of medium-run adaptive and short-run forward looking
expectations. Simulations of the model with our estimated parameters reveal global instability of its steady state. We
show that monetary policy can stabilize the dynamics to some extent and that, in addition, an institutionally given kink
in the money wage Phillips-Curve (downwardly rigid wages) represents a powerful mechanism for obtaining bounded, more
or less irregular fluctuations in the place of purely explosive ones. The resulting fluctuations can be reduced in size
by choosing the parameters of monetary policy within a certain corridor, the exact position of which may however be rather
uncertain.
Asada, T., Chiarella, C., Flaschel, P. & Franke, R. 2003, 'Interacting Two-Country Business Fluctuations'.
In this paper we investigate the closed-economy Keynes-Wicksell-Goodwin model of Chiarella and Flaschel (2000)
for the case of two interacting open economies. We introduce these coupled two-country KWG dynamics on the extensive
form level by means of a subdivision into nine modules describing the behavioral equations, the laws of motion and the
identities or budget equations of the model. We then derive their intensive form representation and the 10 laws of
motions of the model on the basis of certain simplifying asumptions. Thereafter we present the uniquely determined
steady state solution of the dynamics and discuss in a mathematically informal way its stability properties, concerning
asymptotic stability and loss of stability by way of super- or subcritical Hopf-bifurcations. In a final section we
explore numerically a variety of situations of interacting real and financial cycles, where the steady state is locally
repelling, but where the overall dynamics are bounded in an economically meaningful domain by means of a kinked money
wage Phillips curve, exhibiting downward rigidity of the money-wage, coupled with upward flexibility of the usual type.
Chiarella, C., Dieci, R. & Gardini, L. 2003, 'A dynamic analysis of speculation across two markets (QFRC paper #89)'.
Chiarella, C., Flaschel, P., Franke, R. & Semmler, W. 2003, 'Output and the Term Structure of Interest Rates: Ways Out of th Jump-Variable Conundrum'.
In this paper we reconsider a model of Blanchard and Fisher which reformulated Keynesian IS-LM analysis from
the perspective of a richer array of financial assets, namely short-term and long-term bonds, and thus from the
perspective of the term structure of interest rates. The basic change in this extension of the IS-LM approach is that
investment demand (and also consumption demand) now depend on the long-term rate of interest in the palce of the
short-term rate. This implies that the IS-curve and the LM-curve are no longer situated in the same diagram, but have
to be linked via the dynamics of long-term bond prices (in the approach of Blanchard and Fischer based on perfect
substitutes, perfect foresight and the jump variable technique), thereby creating one of the links for the real-financial
interaction to be investigated, the dynamic multiplier process and thw conventional LM curve representing the other one.
Based on this dynamic interaction of real and financial markets we will reflect the outcomes achieved by Blanchard and
Fischer from the perspective of imperfect substitutes and mypoic perfect foresight. We derive on this basis alternatives
to the conventional jump variable technique and its treatment of unanticipated and anticipated monetary and fiscal
policy, which are global in nature and do not depend on well-behaved stable manifolds in an essentially local analysis
of saddlepoint instability as in the case for the jump variable technique.
Chiarella, C., Flaschel, P. & Semmler, W. 2003, 'Real-Financial Interaction: Implications of Budget Equations and Capital Accumulation'.
We investigate the real-financial interaction of an approach of Blanchard to stock market and multiplier
dynamics from the stock-flow consistency perspective by including the capacity and the financing effect of the
investment decision of firms into the model. We show that the steady state solutions of the Blanchard approach
are no longer of relevance here, but rather are replaced by a unique interior long-run solution. We demonstrate
asymptotic stability with respect to this steady state when stock market adjustments is sufficiently sluggish, and
this even in the case of myopic perfect foresight. In the opposite situation, if stock markets adjustments is made
sufficiently fast, the system loses stability by way of a Hopf bifurcation for increasing adjustment speeds of capital
gains expectations and will generate purely explosive behavior shortly thereafter. We indicate for this case how a
regime (or phase diagram) switching methodology between activated and tranquil stock market behavior may nevertheless
ensure global viability of the dynamics, despite the occurence of shorter of longer episodes of explosive financial
acceleration, by assuming that stock markets must return to tranquillity after certain thresholds are passed, where
financial acceleration due to high adjustment speeds in the market for equities disappear.
Chiarella, C., Flaschel, P. & Zhu, P. 2003, 'The Structure of Keynesian Macrodynamics: A Framework for Future Research'.
This paper integrates a number of traditional but partial insights of Keynesian macrotheory into a consistent
whole, with all budget restrictions of all sectors carefully specified, a complete set of stock-flow interactions and
the construction of a unique interior steady state. We provide detailed representations of the many feedback chains and
their interaction that are present in the model. The paper provides proper foundations of a detailed analysis of the
important macroeconomi features that characterize modern large economies.
Chiarella, C. & Flaschel, P. 2003, 'Towards Applied Disequilibrium Growth Theory: V Housing Investment Cycles, Private Debt Accumulation and Deflation'.
In this paper we reconsider a general disequilibrium model of an applied orientation, exhibiting a detailed
modelling of the private housing sector, which we have developed in a series of working papers starting from the Murphy
model for the Australian economy. This modelling approach is complete with respect to budget equations and stock-flow
interactions and can be reduced to a somewhat simplified 18D core model, the dynamics of which was intensively studied
in the earlier work. In the present paper we modify this type of model towards the explicit consideration of debtor and
creditor households which extends the dynamics of the core model by 1 to 19D by the addition of the dynamics of the
debt to capital ratio of indebted households. Various subdynamics of these 19D dynamics are investigated theoretically
and illustrated numerically. The basic findings are that there is convergence to the balanced growth path of the model
for sluggish disequilibrium adjustment processes, that persistent investment cycles in the housing sector can be
generated for certain higher adjustment speeds by way of Hopf-bifurcations in particular. Furthermore processes of debt
deflation my trigger monotonic depressions that get more and more severe when the real debt of debtor households is
systematically increased by deflationary spirals in the goods manufacturing sector in particular.
Chiarella, C., Flaschel, P., Groh, G., Koper, C. & Semmler, W. 2003, 'Towards applied disequilibrium growth theory: V housing investment cycles, private debt accumulation and deflation (F&E paper #97)'.
Chiarella, C., He, X.-.Z. & Zhu, P. 2003, 'Fading Memory Learning in the Cobweb Model with Risk Averse Heterogeneous Producers'.
This paper studies the dynamics of the traditional cobweb model with risk averse heterogeneous producers who seek to learn the distribution of asset prices using a geometric decay processes
(GDP) - the expected mean and variance are estimated as a geometric weighted average of past observations - with either finite or infinite fading memory. With constant absolute risk aversion, the dynamics
of the model can be characterized with respect to the length of memory window and the memory decay rate of the learning GPD. The dynamics of such heterogeneous learning processes and capability of
producers' learning are discussed. It is found that the learning memory decay rate of the GDP of heterogeneous producers plays a complicated role on the pricing dynamics of the nonlinear cobweb model.
In general, an increase of the memory decay rate plays stabilizing role on the local stability of the steady state price when the memory is infinite, but this role becomes less clear when the memory is
finite. It shows a double edged effect of the heterogeneity on the dynamics. It is shown that (quasi)periodic solutions and strange (or even chaotic) attractors can be created through Neimark-Hopf
bifurcation when the memory is infinite and through flip bifucation as well when the
memory is finite.
Chiarella, C., Flaschel, P. & Zhu, P. 2003, 'Towards Applied Disequilibrium Growth Theory: IV Numerical Investigations of the Core 18D Model'.
In this paper we investigate, from the numerical perspective, the 18D core dynamics of a theoretical 39D
representation of an applied disequilibium model of monetary growth of a small open economy. After considering the
model from the viewpoint of national accounting, we provide a compact description of the intensive form of the model,
its laws of motion and accompanying algebraic expressions and its unique interior steady state solution. We then give
a survey of various types of subsystems that can be decomposed from the integrated 18D dynamics by means of suitable
assumptions and also survey the feedback channels that can typically be found in these decomposed or re-integrated model
types. These subsystems and their partial or full integration are investigated and compared in the remainder of the
paper from the perspective of bifurcation diagrams that separate situations of asymptotic stability from stable
cyclical behavior as well as pure explosiveness. In this way we lay the foundations for future extensions of the paper,
which will show, in contract to what is generally believed to characterize structural macroeconomic models, that applied
integrated macrodynamical systems can have a variety of interesting attractors and transients to them. Such attractors
are obtained in particular when locally explosive situations are turned into bounded dynamics by the addition of
specifically tailored extrinsic nonliearities.
Chiarella, C. & Gao, S. 2002, 'Solving the Price-Earnings Puzzle'.
Accounting and finance professionals have empirically known that in the long run stock prices are roughly
proportional to earnings. However, econometric testing could not been able to verify this expected contribution of
earnings to stock prices, thus formed the price-earnings (PE) puzzle in the accounting literature. This paper seeks to
solve this puzzle by allowing the earnings response coefficient to be a variable instead of a constant, and shows that
the PE puzzle turns out to be a phenomenon of type I spurious regression in econometrics.
Chiarella, C. & Gao, S. 2002, 'Type I Spurious Regression in Econometrics'.
In applied econometrics researchers often infer the relation among nonstationary time series by regression of
their differences. The aim of this paper is to show that in some circumstances regression of differenced time series
tends to reject the relation among their levels. This phenomenon is known as type I spurious regression. Time series
are dynamic processes, and the ignored system dynamics will become the systematic errors in regression equations.
Differencing does not preserve the underlying relation among time series in regression due to systematic errors. This
paper will outline how regression of differenced time series tends to reject the relation between their levels, and so
potentially to incur type I spurious regression.
Chiarella, C., Flaschel, P., Franke, R. & Semmler, W. 2002, 'Stability Analysis of a High-Dimensional Macrodynamic Model of Real-Financial Interaction: A Cascade of Matrices Approach'.
This paper analyzes a high-dimensional macrodynamic model of the real-financial interaction. Regarding the
financial sector it focuses on the stock market dynamics, whilst for the real sector it details goods market
disequilibrium and two Phillips curves for prices as well as wages. The central link between the two sectors is
constituted by Tobin's (average) q. The integrated dynamics of the model constitute a seven-dimensional system of
differential equations, the stability analysis of which is the main contribution of the paper. The analysis proceeds
by constructing a cascade of stable matrices and thus demonstrating that the long-run equilibrium is locally stable if
certain adjustments are sufficiently sluggish. Large values of some reaction parameters, on the other hand, can
destabilize the economy, while a Hopf bifurcation analysis shows the potential for cyclical motion in such circumstances.
Chiarella, C. & He, X. 2002, 'An adaptive model on asset pricing and wealth dynamics with heterogeneous trading strategies', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 84 Abstract: This paper develops an adaptive model on asset pricing and wealth dynamic of a financial market with heterogeneous agents and examines the profitability of momentum and contrarian trading strategies. In order to characterize asset price, wealth dynamics and rational adaptiveness arising from the interaction of heterogeneous agents with CRRA utility, an adaptive discrete time equilibrium model in terms of return ad wealth proportions (among heterogeneous representative agents) is established. Taking trend followers and contrarians as the main hetergeneous agents in the model, the profitability of momentum and contrarian trading strategies is analyzed. Our results show the capability of the model to characterize some of the existing evidence on many of anomailies observed in financial markets, including the profitability of momentum trading strategies over short time intervals, rational adaptiveness of agents, overconfidence and underreaction, overreaction and herd behavior, excess volatility, and volatility clustering.
Chiarella, C. & Ziogas, A. 2002, 'Evaluation of American strangles', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 83 Abstract: This paper presents a generalisation of McKean's free boundary value problem for American options by considering an American strangle position, where the early exercise of one side of the payoff will knock-out the out-of-the-money side. When attempting to evaluate the price of this American strangle, it is not correct to simply price the component American call and put options which make up the strangle, and take the sum of their values. The Fourier transform technique is used to derive the integral equation for the price of our American strangle. From this expression, a coupled integral equation system for the strangle's call- and put-side free boundaries is found. While the equation for the price of the strangle is simply the sum of its component American call and put option equations, the free boundary for each side is shown to have a more complex nature. Anumerical algorithm for solving the coupled integral equation system for the free boundaries is provided, and the resulting approximations are used to determine the price of the American strangle position. Numerical comparisons between the strangle price and the price of a portfolio formed from a long position in both an American call an American put option are presented.
Bhar, R., Chiarella, C. & To, T. 2002, 'A maximum likelihood approach to estimation of Heath-Jarrow-Morton models', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 80 Abstract: Research on the Heath-Jarrow-Morton (1992) term structure models so far has focused on the class having time-deterministic instantaneous forward rate volatility. In this case the forward rate is Markovian, even if the spot rate process is not. However, this Markovian feature can only be used under the historical measure, involving two unsatisfactory assumptions: one on market price risk, usually made for pure mathematical tractability, the other to use futures yields as a proxy for the instantaneous forward rate, which may result in estimation bias. This paper circumvents both of these assumptions. First, the bias is quantified and shown to be non-negligible. Then futures contracts are treated as derivative instruments written on forward rates to derive the full information maximum likelihood estimator for observable futures prices, using both time series and cross-sectional data, without the need to assume and estimate any functional forms for the market price of interest rate risk. The derivation involves the likelihood transformation method of Duan (1994). The method is then applied to the estimation of a humped forward rate volatility model for Eurodollar futures series traded on the Chicago Mercantile Exchange.
Chiarella, C. & Gao, S. 2002, 'Modelling the Value of the S&P 500 - A System Dynamics Perspective'.
This paper seeks to model the adjustment process in the stock market by a continuous time state space model
focusing on input-out relations. The value of the S&P 500 is generated as the output of the model with earnings and
the interest rate as input. The model is found to fit the data well, and indicates that the stock price dynamics can
be considered as a price-following-value process. The value determines the time varying trend of price, and random
buy-sell pressure drives price fluctuations about value. The 1987 stock price bubble shows up clearly as a gap between
price and value.
Chiarella, C., Pasquali, S. & Runggaldier, W.J. 2001, 'On filtering in Markovian yerm structure models (An approximation approach)', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 65 Abstract: We study a nonlinear filtering problem to estimate, on the basis of noisy observations of forward rates, the market price of interest rate risk as well as the parameters in a particular term structure model within the Heath-Jarrow-Morton family. An approximation approach is described for the actual computation of the filter.
Bhar, R., Chiarella, C. & Runggaldier, W. 2001, 'Filtering Equity Risk Premia From Derivative Prices'.
This paper considers the measurement of the equity risk premium in financial markets. While there exists a vast amount of research into its behaviour, particularly in US markets, this is largely
based on regression based techniques which do not capture well the dynamic and forward looking nature of the risk premium. In this paper the time variation of the unobserved risk premium is modelled by a
system of stochastic differential equations connected by arbitrage arguments between the spot equity market, the index futures and options on index futures. Although various processes for the
dynamics of the risk premium may be considered, we motivate and analyse a mean-reverting form. Since the risk premium is not directly observable, information on it is extracted using an unobserved
component state space formulation of the system and Kalman filtering methodology. In order to cater for the time variation of volatility we use the option implied volatility in the dynamic equations for
the index and its derivatives. This quantity is in a sense treated as a signal that impounds the market's forward looking view on the equity risk premium. The results using monthly Australian and U.S.
market data over a period of five years are presented. The model fit is found to be statistically significant for both markets. The time series of the mean and standard deviation of the risk premia
generated by the Kalman filter are compared with premia computed from ex-post returns. It is found that the ex-post risk premia have a general tendency to lie within a two standard deviations band around
the filteredmean. However there are frequent movements outside the band, particularly on the downside, indicating that the ex-post measure may be understating the risk premium.
Bhar, R., Chiarella, C. & Runggaldier, W.J. 2001, 'Estimation in models of the instantaneous short term interest rate by use of a dynamic Bayesian algorithm', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 68 Abstract: This paper considers the estimation in models of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we set up the stochastic dynamics for the discretely compounded market observed rates and propose a dynamic Bayesian estimation algorithm (i.e. a filtering algorithm) for a time-discretised version of the resulting interest rate dynamics. The filter solution is computed via a further spatial discretization (quantization) and the convergence of the latter to its continuous counterpart is discussed in detail. The method is applied to simulated data and is found to give a reasonable estimate of the conditional density function and to be not too demanding computationally.
In order to characterize asset price and wealth dynamics arising from the interaction of heterogeneous agents with CRRA utility, a discrete time stationary model in terms of return and wealth
proportions (among different types of agents) is established. When fundamentalists and chartists are the main heterogeneous agents in the model, it is found that in the presence of heterogeneous agents
the stationary model can have multiple steady-states. The steady-state is unstable when the chartists extrapolate strongly and (locally) stable when they extrapolate weakly. The convergence to
steady-state follows an optimal selection principle - the return and wealth proportions tend to the steady-state which has relatively higher return. More importantly, heterogeneity can generate instability
which, under the stochastic processes of the dividend yield and extrapolation rates, results in switching of the return among different states, such as steady-state, periodic and aperiodic cycles from
time to time. To model that is finally developed displays the essential characteristics of the standard asset price dynamics model assumed in continuous time finance, in that the asset price is
fluctuating around a geometrically growing trend. The model also displays the volatility clustering that is an essential feature of empirically observed assets returns.
Chiarella, C. & He, X. 2001, 'Dynamics of beliefs and learning under aL processes - The heterogeneous case', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 55 Abstract: This paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some recursive processes with bounded memory. Under the assumptions of heterogeneous expectations (or beliefs) and that the agents update their expectations by recursive L- and general aL-processes, the dynamics of the resulting expectations and learning schemes are analyzed. It is shown that the dynamics of the system, including stability, instability and bifurcation, are affected differently by the recursive processes. The cobweb model with a simple heterogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics. In particular, the double edged effect of heterogeneity on the dynamics of the model is demonstrated.
Chiarella, C. & He, X. 2001, 'Dynamics of beliefs and learning under aL processes - The homogeneous case', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 53 Abstract: This paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some learning process. Under the assumptions that agents have homogeneous expectations (or beliefs) and that they update their expectations by least-squares L- and general aL - processes, the dynamic of the resulting expectations and learning schemes are analyzed. It is shown how the dynamics of the system, including stability, instability and bifurcation, are affected by the learning processes. The cobweb model with a simple homogeneous expectation scheme is employed as an example to illustrate the stability results, the various types of bifurcations and the routes to complicated price dynamics.
Chiarella, C. & Kwon, O.-.K. 2001, 'State Variables and the Affine Nature of Markovian HJM Term Structure Models'.
Finite dimensional Markovian HJM term structure models provide an ideal setting for the study of term structure dynamics and interest rate derivatives where the flexibility of the HJM framework
and the tractability of Markovian models coexist. Consequently, these models became the focus of a series of papers including Carverhill (1994), Ritchken and Sankarasuramanian (1995), Bhar and Chiarella
(1997), Inui and Kijima (1998) and de Jong and Santa-Clara (1999). In Chiarella and Kwon (2001b), a common generalisation of these models was obtained in which the components of the forward rate volatility
process satisfied ordinary differential equations in the maturity variable. However, the generalised models require the introduction of a large number of state variables which, at first sight, do not appear
to have clear links to market observed quantities. In this paper, it is shown that the forward rate curves for these models can often be expressed as affine functions of the state variables, and conversely
that the state variables in these models can often be expressed as affine functions of a finite number of benchmark forward rates. Consequently, for these models, the entire forward rate curve is not only
Markov but affine with respect to a finite number of benchmark forward rates. It is also shown that the forward rate curve can be expressed as an affine function of a finite number of yields which are
directly observed in the market. This property is useful, for example, in the estimation of model parameters. Finally, an explicit formula for the bond price in terms of the state variables, generalising
the formula given in Inui and Kijima (1998), is provided for the models considered in this paper.
Chiarella, C., Dieci, R. & Gardini, L. 2001, 'Speculative Behaviour and Complex Asset Price Dynamics'.
This paper analyses the dynamics of a model of a share market consisting of two groups of traders: fundamentalists, who form rational expectations on the fundamental value of the asset, and
chartists, who base their trading decisions on an analysis of past price trends. The model is reduced to a two-dimensional map whose dynamic behaviour is analysed in detail, particularly with respect to
global dynamical behaviour. The dynamics are affected by parameters measuring the strength of fundamentalist demand and the speed with which chartists adjust their estimate of the trend to past price
changes. The parameter space is characterized according to the local stability/instability of the equilibrium point as well as the noninvertibility of the map. The method of critical curves of
noninvertible maps is used to understand and describe the range of global bifurcations that can occur. It is also shown how the knowledge of deterministic dynamics uncovered here can aid in understanding
stochastic versions of the model.
Chiarella, C., Flaschel, P., Franke, R. & Semmler, W. 2001, 'Real-Financial Interaction: Integrating Supply Side Wage-Price Dynamics and the Stock Market'.
The paper put forward a macrodynamic model of the real-financial interaction. Regarding the financial sector it
focuses on the stock market dynamics, for real sector it details goods market disequilibrium and two Phillips curves for
prices as well as wages. The central link between the two sectors is constituted by Tobin's (average) q. After
highlighting the main feedback mechanisms in the real and financial subdynamics, the long-run equilibrium of the
integrated 7th-order dynamic system is shown to be locally stable if certain adjustments are sufficiently sluggish,
while large values of some reaction parameters can destabilize the economy. Lastly, the analysis reveals the potential
for cyclical motion.
Chiarella, C. & Kwon, O.-.K. 2000, 'A Class of Heath-Jarrow-Morton Term Structure Models with Stochastic Volatility'.
This paper considers a class of Heath-Jarrow-Morton term structure models with stochastic volatility. These models admit transformations to Markovian systems, and consequently lend themselves to
well-established solution techniques for the bond and bond option prices. Solutions for certain special cases are obtained, and compared against their non-stochastic counterparts.
Bohm, V. & Chiarella, C. 2000, 'Mean variance preferences, expectations formation, and the dynamics of random asset prices', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 46 Abstract: This paper analyzes the dynamics of a general explicit random price process of finitely many assets in an economy with overlapping generations of heterogeneous consumers forming optimal portfolios, extending the one dimensional investigation of Bohm, Deutscher and Wenzelburger (2000). Consumers maximize expected utility with respect to subjective transition probabilities defined by Markov kernels. Given a forecasting rule (predictor) and an exogeneous stochastic process of producer dividends, the dynamics of the economy is described as a random dynamical system in the sense of Arnold (1998). The paper investigates existence and stability of random fixed points (invariant measures) for mean-variance preferences under various forecasting schemes, including unbiased predictions as well as OLS forecasting. Numerical simulations show the stability and the performance of the different predictors for linear mean-variance preferences. Alternative random dividend processes are provided.
Chiarella, C. & Kwon, O. 2000, 'A complete stochastic volatility model in the HJM framework', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 43 Abstract: This paper considers a stochastic volatility version of the Heath, Jarrow and Morton (1992) term structure model. Market completeness is obtained by adapting the Hobson and Rogers (1998) complete stochastic volatility stock market model to the interest rate setting. Numerical simulation for a special case is used to compare the stochastic volatility model against the traditional Vasicek (1977) model.
Bhar, R. & Chiarella, C. 2000, 'Infering Forward Looking Financial Market Risk Premia from Derivatives Prices'.
This paper focuses on a topical and important area of theory and practice ie. The risk premium in financial markets. While there exists a vast amount of research into its behaviour, particularly
in US markets, this is largely based on regression based techniques which do not capture well the dynamic and forward looking nature of the risk premium.
In this paper the variation of the unobserved risk premium is modelled by a system of stochastic differential equations connected by arbitrage arguments between the spot equity market, the index futures
and options on index futures. Although various processes for the dynamic of the risk premium may be considered, we motivate and analyse a mean-reverting form. The diffusion part is specified such that the
risk premium remains positive. Since the risk premium is not directly observable, information on it is extracted using an unobserved component state space formulation of the system and filtering
methodology. As an initial application of the methodology, the results from daily Australian market data from the SFE over a period of twelve months are presented. The small sample properties of the
parameter estimates are also examined by bootstrapping the state space system. It is well known in the filtering literature that the estimation of state space system by Kalman filter is sensitive to the
specification of the quantities such as initial state variables and the prior covariance matrix. The paper also carries out approximate sensitivity analysis in this respect.
Bhar, R., Chiarella, C. & Pham, T. 2000, 'Modeling the Currency Forward Risk Premium: Theory and Evidence'.
There is a huge literature on the existence of risk premia in the foreign exchange markets and its influence in explaining the divergence between the forward exchange rate and the subsequently
realised spot exchange rate. In this paper, we seek to model directly the risk premium as a mean-reverting diffusion process. This is done by making use of the spot-forward price relationship and assuming
a geometric Brownian process for the spot exchange rate. We are able to obtain a stochastic differential equation system for the spot exchange rate, the forward exchange rate and the risk premium which we
estimate using Kalman filtering techniques. The model is then applied to the French Franc/USD and Japanese Yen/USD exchange rates from 1 January 1990 to 31 December 1998. For both currencies our main
findings show (I) the persistence of substantial positive time variation in the forward risk premium and its alternating regimes; and (ii) the presence of a term structure of the forward risk premia.
We analyse the procedure for determining volatility presented by Lagnado and Osher, and explain in some detail where the scheme comes from. We present an alternative scheme which avoids some of
the technical complications arising in Lagnado and Osher's approach. An algorithm for solving the resulting equations is given, along with a selection of numerical examples.
The paper studies a class of models in which agents' expectations influence the actual dynamics while the expectations themselves are the outcome of some learning processes. Situations of both
homogeneous and heterogeneous beliefs are considered. In both cases agents update their expectations by general ah - and least-squares h-processes and the stability of the resulting dynamics in both cases
is analysed. It is shown how the stability of the actual dynamics is affected by the heterogeneous expectations and different least-squares h-processes.
Bhar, R., Chiarella, C., El-Hassan, N. & Zheng, X. 2000, 'The Reduction of Forward Rate Dependent Volatility HJM Models to Markovian Form: Pricing European Bond Option'.
We consider a single factor Heath-Jarrow-Morton model with a forward rate volatility function depending upon a function of time to maturity, the instantaneous spot rate of interest and a forward
rate to a fixed maturity. With this specification the stochastic dynamics determining the prices of interest rate derivatives may be reduced to Markovian form. Furthermore, the evolution of the forward
rate curve is completely determined by the two rates specified in the volatility function and it is thus possible to obtain a closed form expression for bond prices. The prices of bond options are
determined by a partial differential equation involving two spatial variables. We discuss the evaluation of European bond options in this framework by use of the ADI method.
Chiarella, C. & He, X. 2000, 'Heterogeneous beliefs, risk and learning in a simple asset pricing model with a market maker', Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney.
Research Paper Number: 35
Bhar, R. & Chiarella, C. 2000, 'Approximating Heath-Jarrow-Morton Non-Markovian Term Structure of Interest Rate Models with Markovian Systems'.
We consider a Heath-Jarrow-Morton models for the term structure of interest rates in which the forward rate
volatility is a function of the instantaneous spot rate of interest, a set of dicrete forward rates and time to maturity
of the bond. We show how the stochastic dynamics may be expressed as a system of Markovian stochastic differential
equations. We obtain the partial differential equation which allows the pricing of contingent claims in this framework.
Chiarella, C., Flaschel, P., Franke, R. & Semmler, W. 2000, 'Output, Financial Markets and Growth'.
In this paper we reconsider a macrodynamic model of Blanchard, which integrates output and stock market dynamics
in a fundamental way. We add budget equations (and their implications) to all sectors of the economy, and also capital
accumulation and growth (but not yet proper wage-price dynamics) and obtain a model of the real-financial interaction
with quite different steady state characteristics as compared to the Blanchard approach. We furthermore allow for
somewhat sluggish adjustment of share prices and capital gain expectations in place of perfect substitutes and perfect
foresight. This brings our approach closer to completion and also makes it much more involved. Instead of the originally
only 2D dynamics we now obtain a 4D dynamical system with two real and two financial variables and specific stability
properties. However, by setting certain secondary expressions equal to their trend values, we can regain the mathematical
form of the original 2D dynamics of Blanchard type. This form is now based on variables that allow for stationarity,
when estimated, that therefore permit to estimate the model to get information about the magnitude of its adjustment
speeds, the size of which is crucial for the stability of instability of this dynamical system.
Chiarella, C. & El-Hassan, N. 1999, 'Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines'.
We consider the pricing of American bond options in a Heath-Jarrow-Morton framework in which the forward rate volatility is a function of time to maturity and the instantaneous spot rate of
interest. We have shown in Chiarella and El-Hassan (1996) that the resulting pricing partial differential operators are two dimensional in the spatial variables. In this paper we investigate an
efficientnumerical method to solve there partial differential equations for American option prices and the corresponding free exercise surface. We consider in particular the method of lines which other
investigators (eg Carr and Faguet (1994) and Van der Hoek and Meyer (1997)) have found to be efficient for American option pricing when there is one spatial variable. In extending this method for the two
dimensional case, we solve the pricing equation by discretising the time variable and one state varialbe and using the spot rate of interest as a continuous variable. We compare our method with the lattice
method of Li, Ritchken and Sankarasubramanian (1995).
Chiarella, C. & Flaschel, P. 1999, 'Towards Applied Disequilibrium Growth Theory: III Basic Partial Feedback Structures and Stability Issues'.
In this paper we consider the 18D case model of applied disequilibrium growth whose extensive and intensive
form dynamics we derived in earliier work. Here we analyze in particular the basic partial feedback mechanisms whose
interaction drives the dynamics of the overall model. We relate these mechanisms with the names of the economists who
originally identified them (usually as isolated mechanisms) e.g., Goodwin, Rose, Keynes, Tobin, Dornbusch and Blanchard.
A large part of our analysis is devoted to a study of the factors causing these mechanisms to display stabilizing or
destabilizing tendencies. We also discuss some nonlinear mechanisms which may 'tame' the explosive tendencies of the
economy in situations of local instability.
Chiarella, C. & Flaschel, P. 1999, 'Towards Applied Disequilibrium Growth Theory: II Intensive Form and Steady State Analysis of the Model'.
In this paper we investigate further the 34D applied structural model whose extensive form we introduced
in Chiarella and Flaschel (1999c). Here we express the model in terms of intensive form state variables, thereby
abstracting from the underlying growth trend. We explain the dynamic (and static) laws of the model directly in terms
of the intensive form variables, and then determine the steady state and its characteristics. Finally we show how a small
number of simplifying assumptions, concerning in particular consumption of asset holders and some secondary adjustment
processes, reduce the 34D model to an 18D core model. It is this latter core model whose detailed structure, steady state
characteristics and dynamical behavior will become the object of study in the remaining papers of this sequence.
Chiarella, C. & Flaschel, P. 1999, 'Towards Applied Disequilibrium Growth Theory: I The Starting Model'.
In this paper we build a hierarchically structured continuous-time model of Keynesian monetary growth. The
model is sufficiently rich with respect to markets, sectors and agents and consistent with respect to budget constraints
to capture sufficient broad details of actual macroeconomies and so serve as a macrotheoretic basis for many large scale
models. We describe the model at the level of national accounts and then derive its extensive form dynamics. We also give
detailed discussion as to how our model is related to the large scale Murphy model of the Australian economy. Our model
provides a basis for understanding the various economic feedback chains contained in such models and their dynamic
interaction.
Chiarella, C. & Flaschel, P. 1999, 'Disequilibrium Growth Theory: Foundations, Synthesis, Perspectives'.
In this paper we survey, also for the general reader interested in the non-market cleaning approach to growth
and fluctuations, the foundations, the core model and the general framework underlying our joint work on integrated
disequilibrium models of monetary growth, drawing also on joint work with further co-authors in various places. We found
the basic working model of this type on appropriately reformulated and extended partial dynamic models already existing
in the literature. We then develop the obtained working model further into a theoretical continuous-time disequilibrium
growth model of a very general nature. We then show that there are strong relationships between our general model and
models currently used for structural macroeconomic model-building and their applications. In this way we want to
contribute both to the further development and analysis of full-sized theoretical models of disequilibrium growth and to
the theoretical penetration of their modern counterparts in the applied literature. Such development and analysis is based
on detailed steady state analyses, on use of theoretical investigations of all important subdynamics that are there
involved (in isolation as well as in their interaction) and, on computer simulations based on a variety of modern
numerical tools of nonlinear dynamical analysis.
Chiarella, C., Flaschel, P., Groh, G., Köper, C. & Semmler, W. 1999, 'Towards Applied Disequilibrium Growth Theory: VII Intensive Form and Steady State Calculation in the Case of Substitution'.
In this paper we consider the applied structural model of diequilibrium growth that we introduced in a previous
paper. In particular we express the model in terms of intensive form variables which turn out to be governed by a set of
39D dynamic equations. We consider the model from the perspective of national accounts and also determine and analyze
the model's steady state. The model allows for smooth input and output substitution (via a neoclassical production
function) between its three inputs (capital, imported commodities and labor) and two outputs (domestically traded
goods and exported commodities).
Chiarella, C., Flaschel, P., Groh, G., Köper, C. & Semmler, W. 1999, 'Towards Applied Disequilibrium Growth Theory: VI Substitution, Money-Holdings, Wealth-Effects and Further Extensions'.
In this paper we present a theoretical disequilibrium growth model of an open economy with a full set of markets
and sectors and with heterogeneous agents in the household sector. This model allows, on the one hand, for basic
consistency checks, such as fully specified bedget identities and a well-defined steady state refernce path and is
therefore carefully specified from the theoretical point of view. On the other hand, the model is already fairly close
to applied modern structural model building and thus is rich in descriptive detail.
The model exhibits five real and five financial markets. Consumption behavior is formulated by way of the life cycle
hypothesis and savings of worker households are allocated to money and short-term bonds, while savings of pure asset
holders concern all financial assets considered (equities and long-term bonds, domestic and foreign ones). Firms use
three inputs (labor, capital and imports) to produce two outputs (domestic goods and export commodities) by way of a
nested CES/CET technology and they produce in a cost-minimizing way subject to a domestic demand constraint, also
formulating medium run targets that guide their investment and pricing decision. The government sector is described
in a very detailed way, including a variety of taxation schemes in particular and also a debt target according to which
taxes are adjusted. We consider sluggishly adjusting wages and prices, coupled with heterogeneous expectations formation,
and have on this basis fluctuating rates of capacity utilization on the labor market as well as on the market for goods.
Financial markets, finally, are described by delayed adjustment processes towards interest rate parity conditions.
The paper itself presents only the extensive form of the model with all of its details and compares it to the Murphy
model for the Australian economy and also with the Multimod model, Mark III of the IMF. In subsequent papers we derive
the intensive form of ...
Chiarella, C. & El-Hassan, N. 1997, 'A Survey of Models for the Pricing of Interest Rate Derivatives'.
Chiarella, C. & Khomin, A. 1996, 'Learning Dynamics in a Nonlinear Stochastic Model of Exchange Rates'.
This paper considers a version of the Dornbusch model of exchange rate dynamics which allows a nonlinear
domestic demand for foreign assets function and imperfect substitutability between domestic and foreign interest bearing
assets. Expectations of exchange rate changes are modelled as adaptive with perfect foresight being obtained as a limiting
case. For sufficiently rapid speed of adjustment of expectations the model is able to generate cyclical behaviour of the
exchange rate and expectations of its change. In the perfect foresight limit the cycles become relaxation cycles. To this
underlying model of the fundamentals a white noise "news" process is added. Agents are assumed to attempt to learn about
the system dynamics and the link between such learning and exchange rate volatility is studied. Two learning scenarios are
considered. In the first scenario economic agents are regarded as a uniformly well-informed group of sophisticated traders.
In the second scenario a group of "naive" traders coexist with the sophisticated traders. We find that both learning
scenarios lead to increased volatility. However this effect increases in proportion to the weight of the "naive" traders.
Bhar, R. & Chiarella, C. 1996, 'Bootstrap Results From the State Space From Representation of the Heath-Jarrow-Morton Model'.
This paper builds upon the authors' previous work on transformation of the Heath-Jarrow-Morton (HJM) model of the
term structure of interest rates to state space form for a fairly general class of volatility specification including
stochastic variables. Estimation of this volatility function is at the heart of the identification of the HJM model. The
paper develops a bootstrap procedure for the HJM model cast into the non-linear filtering framework to analyse the
statistical significance of the estimators. It is shown that not all combinations of the parameters of the volatility
function are equally likely. The procedure also reveals distributional properties of the instantaneous spot rate of
interest implied by the HJM model.
Bhar, R. & Chiarella, C. 1996, 'Construction of Zero-Coupon Yield Curve From Coupon Bond Yield Using Australian Data'.
This paper briefly surveys the various approaches to modelling the zero coupon yield curve is the starting point
for much finance research. The method adopted here for the Australian Treasury bond data is based upon polynomial spline
fitting, but with the constraint that the long end of the term structure is stable. This approach has also been
successfully applied to the Danish bond market (Tanggaard and Jakobsen (1988)). The forward rate curve then becomes the
important input data for the modelling of the term structure of interest rates and pricing of interest rate contingent
claims using the Heath-Jarrow-Morton (1992) model.
Chiarella, C. & Flaschel, P. 1995, 'Keynesian Monetary Growth Dynamics: The Missing Prototype'.
Chiarella, C. & Okuguchi, K. 1995, 'A Dynamic Analysis of Cournot Duopoly in Imperfectly Competitive Product and Factor Markets'.
Assuming identical firms, a linear market demand function and a single factor of production, labour, we analyse
the existence and stability of a homogeneous Cournot duopoly facing imperfect competition in both product and factor
markets. Under the assumption of a fairly general wage function we are able to demonstrate local stability of the unique
equilibrium, and global stability under the assumption of a convex reaction function.
Bhar, R. & Chiarella, C. 1995, 'Transformation of Heath-Jarrow-Morton Models to Markovian Systems'.
A class of volatility functions for the forward rate process is considered, which allows the bond price dynamics
in the Heath-Jarrow-Morton (HJM) framework to be reduced to a finite dimensional Markovian system. The use of this
Markovian system in estimation of parameters of the volatility function via use of the Kalman filter is discussed.
Further, the Markovian system allows the link to be drawn between the HJM and the Vasicek/Cox-Ingersoll-Ross (CIR)
frameworks for modelling the term structure of interest rates.
Bhar, R. & Chiarella, C. 1995, 'Estimating the Term Structure of Volatility in Futures Yield - A Maximum Likelihood Approach'.
The volatility structure of 90-day bill futures traded on the the Sydney Futures Exchange is analysed within the
framework of the Heath-Jarrow-Morton model. The method involves characterisation of the transition probability density
function for the forward rate process represented by the stochastic differential equation in the arbitrage-free economy.
Maximisation of the likelihood function then results in the estimates of the parameters of the volatility function. The
volatility function is also used in a simulation of the preference-free stochastic differential equation for bill prices.
Chiarella, C. 1992, 'The dynamics of speculative behaviour', Baltzer Science Publishers, Baarn/Kluwer Academic Publishers, pp. 101-123.
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A number of recent empirical studies cast some doubt on the random walk theory of asset prices and suggest these display significant transitory components and complex chaotic motion. This paper analyses a model of fundamentalists and chartists which can generate a number of dynamic regimes which are compatible with the recent empirical evidence. © 1992 J.C. Baltzer AG, Scientific Publishing Company.
Chiarella, C. 1992, 'Developments in Nonlinear Economic Dynamics: Past, Present and Future'.
Chiarella, C. 1991, 'The Birth of Limit Cycles in Cournot Oligopoly Models with Time Delays'.
We consider the fate of output in the Cournot oligopoly model when the equilibrium is locally unstable. We discuss types of nonlinearities which may be present to bound the motion and introduce time lags in production and
information which may serve as bifurcation parameters. In the case of identical firms we apply the Hopf bifurcation theorem to determine conditions under which limit cycle motion is born.
Chiarella, C. 1991, 'Monetary and Fiscal Policy Under Nonlinear Exchange Rate Dynamics'.
A nonlinear exchange rate model based on the famous Dornbusch (1976) overshhoting model is modified to allow for explicit consideration of the sources of supply and demand in the foreign exchange market along the lines
suggested by Kouri (1983). Imperfect substitutability between domestic and foreign assets and finite speed of adjustment are intorduced into the foreign exchnage market. Portfolio considerations dictate that the function describing
the fraction of wealth domestic residents desire to hold in foreign assets be nonlinear. The exchange rate dynamics are governed by a set of nonlinear differential equations which exhibit limit cycle behaviour under perfect foresight.
A number of fiscal and monetary policies are examined within the framework of the nonlinear model and compared with results with results obtained in the traditional linear mode of analysis.
Chiarella, C., Pham, T., Sim, A.B. & Tan, M. 1991, 'The Interaction of the Financing and Investment Decisions: Preliminary Results in the Australian Context'.
In this paper we report preliminary empirical results on the issue of the interaction of the investment and financing decisions in the Australian context. The investigation was implemented on a sample ranging from 144 to 221
firms for the period from 1980/85. Strong support for the hypothesis that investments and dividends are competing uses of funds, implying presence of interaction, is found for two (1983/84, 1984/85) of the five years under study. Work
is in train to extend the sample period from five to ten years in order to obtain a reasonable persepctive of the distribution of support/non-support for the link between the investment and financing decisions.
Chiarella, C., Iori, G. & Perello, J., 'The Impact of Heterogeneous Trading Rules on the Limit Order Book and Order Flows'.
In this paper we develop a model of an order-driven market where traders set bids and asks and post market or limit orders according to exogenously fixed rules.
Agents are assumed to have three components to the expectation of future asset returns, namely-fundamentalist, chartist and noise trader. Furthermore agents differ in the characteristics describing these components, such as time horizon, risk aversion and the weights given to the various components. The model developed here extends a great deal of earlier literature in that the order submissions of agents are determined by utility maximisation, rather than the mechanical unit order size that is commonly assumed. In this way the order flow is better related to the ongoing evolution of the market. For the given market structure we analyze the impact of the three components of the trading strategies on the statistical properties of prices and order flows and observe that it is the chartist strategy that is mainly responsible of the fat tails and clustering in the artificial price data generated by the model. The paper provides further evidence that large price changes are likely to be generated by the presence of large gaps in the book.
Chiarella, C. & Khomin, A., 'Adaptive Rational Expectations in Models of Monetary Dynamics'.
Chiarella, C. & Flaschel, P., 'Applying Disequilibrium Growth Theory: Debt Effects and Debt Deflation'.
In this paper, we consider two polar dynamical models in which firms use
debt (loans) to finance their investment expenditure: a three-dimensional
supply-driven model and a sophisticated 20-D Keynesian growth model. In
the first, firms' debt accumulations interact with the income distribution
and resulting capital-stock and employment-growth patterns. In the second,
a high-dimensional model, we have sluggishly adjusting prices and
quantities, Keynesian demand rationing, and fluctuating capacity
utilization for both labor and capital -- with all budget equations
specified and a balanced-growth reference path. These polar growth
perspectives are brought together in an intermediate 4-D dynamics, where
the debt accumulation of the simple model is combined with the possibility
of the deflationary processes of the general model. This intermediate case
allows the formulation and investigation, both analytically and
numerically, of situations of debt deflation in a demand-constrained setup
that augments the insights obtained from the simple model and illustrates
an important destabilizing feedback chain in the general 20-D dynamics.
CHEANG, G.E.R.A.L.D.H.L., CHIARELLA, C.A.R.L. & ZIOGAS, A.N.D.R.E.W., 'THE VALUATION OF AMERICAN EXCHANGE OPTIONS UNDER'.
Margrabe provides a pricing formula for an exchange option where the
distributions of both stock prices are log-normal with correlated components. Merton
has provided a formula for the price of a European call option on a single stock where
the stock price process contains a compound Poisson jump component, in addition to
a continuous log-normally distributed component. We use Merton's analysis to extend
Margrabe's results to the case of exchange options where both stock price processes
also contain compound Poisson jump components. We show that there is a change in
the distribution of the jump components in the equivalent martingale measure when
jumps are present in the num´eraire process. In the case of the American version of such
options, the price is shown to be the solution of a free boundary problem. We solve
this problem using a modification of McKean's incomplete Fourier transform method
due to Jamshidian. The resulting integral equation for the early exercise boundary is
solved numerically. We compare the numerical integration solution with a method of
lines approach
Asada, T., Chiarella, C., Flaschel, P. & Franke, R., 'Interacting Two-Country Business Fluctuations'.
In this paper we investigate the closed-economy
Keynes-Wicksell-Goodwin model of Chiarella and Flaschel (2000) for
the case of two interacting open economies. We introduce these
coupled two-country KWG dynamics on the extensive form level by
means of a subdivision into nine modules describing the behavioral
equations, the laws of motion and the identities or budget
equations of the model. We then derive their intensive form
representation and the 10 laws of motion of the model on the
basis of certain simplifying assumptions. Thereafter we present
the uniquely determined steady state solution of the dynamics and
discuss in a mathematically informal way its stability
properties, concerning asymptotic stability and loss of stability
by way of super- or subcritical Hopf-bifurcations. In a final
section we explore numerically a variety of situations of
interacting real and financial cycles, where the steady state is
locally repelling, but where the overall dynamics are bounded in
an economically meaningful domain by means of a kinked money wage
Phillips curve, exhibiting downward rigidity of the money-wage,
coupled with upward flexibility of the usual type.
Charpe, M., Chiarella, C., Flaschel, P. & Proaño, C., 'Business Confidence and Macroeconomic Dynamics in a Nonlinear Two-Country Framework with Aggregate Opinion Dynamics'.
The main objective of the present paper is to investigate explicitly the role of the state of
confidence for the macroeconomic dynamics of two interacting economies using the opinion dy-
namics approach by Weidlich and Haag (1983) and Lux (1995). Particularly, the overall state of
confidence in the world (two-country) economy plays not only for the dynamics of the nominal ex-
change rate but also for the dynamics of the real economy through the determination of aggregate
investment. This novel feature allows us to consider far richer international macroeconomic inter-
actions than most standard models. Further, it features wage-price dynamics that interact with
output and employment fluctuations – leading to a Goodwin (1967)-type of distributive cycle –,
as well as debt dynamics due to a credit-financed investment behavior. The resulting framework
is both advanced as well as flexible enough to generate various types of persistent fluctuations,
and also complex dynamics.