# Dr Christina Nikitopoulos Sklibosios

### Biography

Dr Christina Nikitopoulos joined the School of Finance and Economics in July 2003 and she has been a Senior Lecturer at the UTS Business School since July 2011. She had been with the School for several years before this undertaking her PhD on developing Markovian models for the term structure of interest rates under jump-diffusions. Christina has an extensive experience in teaching within Quantitative Finance with specialization in derivative securities pricing, derivatives and risk management, investments as well as interest rate modelling.

Her research interests include derivative securities pricing, modelling of term structure of interest rates, credit risk modelling, and more recently modelling of commodity futures markets. Christina has published in leading finance journals including Energy Economics, The Journal of Futures Markets, Quantitative Finance and Applied Mathematical Finance.

**Senior Lecturer,**Finance Discipline Group

**Core Member,**QFRC - Quantitative Finance

MBus(UTS), PhD (UTS)

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**Phone**

+61 2 9514 7768

**ORCID**

### Research Interests

Derivative securities pricing, modelling of term structure of interest rates, credit risk modelling, modelling of commodity prices.

**Can supervise:**Yes

Blessing Taruvinga, Benjamin Cheng,

Long Bui, Matthew Squires,

Ke Du, Samuel Chege Maina

Derivative securities pricing, Interest rate modelling and derivatives

## Books

Chiarella, C., Xue-Zhong, H. & Nikitopoulos, C.S. 2015,

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*Derivative Security Pricing Techniques, Methods and Applications*, Springer.View/Download from: UTS OPUS

The book presents applications of stochastic calculus to derivative security pricing and interest rate modelling.

## Chapters

Clewlow, L., Kang, B. & Nikitopoulos Sklibosios, C. 2014, 'On the Volatility of Commodity Futures Prices' in Dieci, R., He, X. & Hommes, C. (eds),

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*Nonlinear Economic Dynamics and Financial Modelling: Essays in Honour of Carl Chiarella*, Springer, pp. 315-334.View/Download from: Publisher's site

## Conferences

Cheng, B., Nikitopoulos Sklibosios, C. & Schlogl, E. 2016, 'Empirical pricing performance on long-dated crude oil derivatives: Do stochastic interest rates matter?', Energy and Commodity Finance Conference, Paris, France.

Nikitopoulos Sklibosios, C., Squires, M., Thorp, S. & Yeung, D.C. 2014, 'The spread seesaw: How consumption, inventory and expected volatility affect the oik forward curve', Frontiers in Financial Econometrics, Brisbane, Australia.

Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2014, 'The return-volatility relation in commodity futures markets', Performance of Financial Markets and Credit Derivatives, Geelong, Australia.

Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2014, 'The Return-Volatility Relation in Commodity Futures Markets', 8th World Congress of Bachelier Finance Society, Brussels, Belgium.

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, Manchester Business School, Manchester, UK.

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.

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.

Nikitopoulos Sklibosios, C. & Platen, E. 2011, 'Alternative term structure models for reviewing expectation puzzles', II World Finance Conference, Rhodes, Greece.

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2009, 'Alternative defaultable term structure models', X Workshop on Quantitative Finance to the Memory of Nicola Bruti-Liberati, Milan, Italy.

Bruti Liberati, N., Nikitopoulos Sklibosios, C. & Platen, E. 2008, 'Monte-Carlo simulations of alternative defaultable term structure models', Bachelier Finance Society 5th World Congress, London, UK.

Nikitopoulos Sklibosios, C., Bruti Liberati, N., Platen, E. & Schlogl, E. 2008, 'Real-world pricing for defaultable term structure models', Bachelier Finance Society 5th World Congress, London, UK.

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2007, 'Real-World Pricing for Defaultable Term Structure Models', CREDIT 2007, Venice, Italy.

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2007, 'Defaultable term structure models under the benchmark approach', Quantitative Methods in Finance 2007 Conference, Sydney, Australia.

Bruti Liberati, N., Nikitopoulos Sklibosios, C. & Platen, E. 2006, 'Heath Jarrow Morton equation for jump-diffusions under the benchmark approach',

*2nd International Symposium on Economic Theory, Policy & Applications*, 2nd International Symposium on Economic Theory, Policy & Applications, -, Athens, Greece. Bruti Liberati, N., Nikitopoulos Sklibosios, C. & Platen, E. 2006, 'On the strong approximation of jump-diffusion processes', Stochastic Calculus and its Applications to Quantitative Finance and Electrical Engineering, Calgary, Canada.

Nikitopoulos Sklibosios, C. 2006, 'Real-world pricing for the HJM framework with jumps',

*Quantitative Methods in Finance 2006 Conference*, Quantitative Methods in Finance 2006 Conference, Sydney, Australia. Nikitopoulos Sklibosios, C. 2006, 'Markovian HJM term structure models under jump-diffusions', Seminar Presentation, Department of Mathematics, University of Patras, Patras, Greece.

Nikitopoulos Sklibosios, C. 2006, 'Benchmark term structure of interest rates under jump-diffusions', Seminar Presentation, Department of Mathematics, University of Patras, Patras, Greece.

Chiarella, C. & Nikitopoulos Sklibosios, C. 2003, 'A class of jump-diffusion bond pricing model within the HJM framework',

*20th AFFI International Conference 2003*, 20th AFFI International Conference 2003, The Association Francaise de Finance, Lyon, France, pp. 1-36. 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., Schlogl, E. & Nikitopoulos Sklibosios, C. 2003, 'A Markovian defaultable term structure model with state dependent volatilities',

*CREDIT 2003 Conference on Dependence Modelling for Credit Portfolios*, --, Venice, Italy. Chiarella, C., Nikitopoulos Sklibosios, C. & Schlogl, E. 2003, 'A Markovian defaultable term structure model with state dependent volatilities',

*Quantitative Methods in Finance 2003 Conference*, Quantitative Methods in Finance 2003 Conference, --, Sydney, Australia. Nikitopoulos Sklibosios, C. 2003, 'Defaultable HJM term structure models', Quantitative Methods in Finance 2003 Conference, Sydney, Australia.

Nikitopoulos Sklibosios, C. 2002, 'A jump diffusion derivative pricing model arising within the Heath-Jarrow-Morton framework',

*Quantitative methods in Finance 2002 Conference*, Quantitative Methods in Finance 2002 Conference, Sydney and Cairns, 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.## Journal articles

Chiarella, C., Kang, B., To, T. & Nikitopoulos Sklibosios, C. 2016, 'The return-volatility relation in commodity futures markets',

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*Journal of Futures Markets*, vol. 36, no. 2, pp. 127-152.View/Download from: UTS OPUS or Publisher's site

Chiarella, C., Maina, S.C. & Nikitopoulos Sklibosios, C. 2013, 'Credit derivatives pricing with stochastic volatility models',

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*International Journal of Theoretical and Applied Finance*, vol. 16, no. 4, pp. 1-28.View/Download from: UTS OPUS or Publisher's site

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 Read More: http://www.worldscientific.com.ezproxy.lib.uts.edu.au/doi/abs/10.1142/S0219024913500192

Nikitopoulos Sklibosios, C. & Platen, E. 2013, 'Alternative term structure models for reviewing the expectations puzzle',

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*International Journal of Economic Research*, vol. 10, no. 2, pp. 349-372.View/Download from: UTS OPUS

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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',

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*Energy Economics*, vol. 40, no. 1, pp. 989-1000.View/Download from: UTS OPUS or Publisher's site

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.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.

Bruti Liberati, N., Nikitopoulos Sklibosios, C. & Platen, E. 2010, 'Real-world jump-diffusion term structure models',

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*Quantative Finance*, vol. 10, no. 1, pp. 23-37.View/Download from: UTS OPUS or Publisher's site

This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event-driven noise is modelled by a Poisson random measure. Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the real-world probability measure. In particular, the real-world dynamics of the forward rates are derived and, for specific volatility structures, finite-dimensional Markovian representations are obtained. Furthermore, allowing for a stochastic short rate in a non-Markovian setting, a class of tractable affine term structures is derived where an equivalent risk-neutral probability measure may not exist

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2009, 'Alternative defaultable term structure models',

View/Download from: UTS OPUS or Publisher's site

*Asia - Pacific Financial Markets*, vol. 16, no. 1, pp. 1-31.View/Download from: UTS OPUS or Publisher's site

The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the existence of an equivalent risk-neutral probability measure is not required. In particular, the real-world dynamics of the instantaneous defaultable forward rates under a jump-diffusion extension of a HJM type framework are derived. Thus, by establishing a modelling framework fully under the real-world probability measure, the challenge of reconciling real-world and risk-neutral probabilities of default is deliberately avoided, which provides significant extra modelling freedom. In addition, for certain volatility specifications, finite dimensional Markovian defaultable term structure models are derived. The paper also demonstrates an alternative defaultable term structure model. It provides tractable expressions for the prices of defaultable derivatives under the assumption of independence between the discounted growth optimal portfolio and the default-adjusted short rate. These expressions are then used in a more general model as control variates for Monte Carlo simulations of credit derivatives.

Chiarella, C., Nikitopoulos Sklibosios, C. & Schlogl, E. 2007, 'A Markovian Defaultable Term Structure Model with State Dependent Volatilities',

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*International Journal of Theoretical and Applied Finance*, vol. 10, no. 1, pp. 155-202.View/Download from: UTS OPUS or Publisher's site

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.

Chiarella, C., Nikitopoulos Sklibosios, C. & Schlogl, E. 2007, 'A Control Variate Method for Monte Carlo Simulations of Heath-Jarrow-Morton Models with Jumps',

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*Applied Mathematical Finance*, vol. 14, no. 5, pp. 365-399.View/Download from: UTS OPUS

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.

Bruti Liberati, N., Nikitopoulos Sklibosios, C. & Platen, E. 2006, 'First order strong approximations of jump diffusions',

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*Monte Carlo Methods and Applications*, vol. 12, no. 3-4, pp. 191-209.View/Download from: UTS OPUS

DP0559879

Bruti-Liberati, N., Nikitopoulos-Sklibosios, C. & Platen, E. 2006, 'First order strong approximations of jump diffusions',

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*Monte Carlo Methods and Applications*, vol. 12, no. 3, pp. 191-209.View/Download from: Publisher's site

This paper presents new results on strong numerical schemes, which are appropriate for scenario analysis, filtering and hedge simulation, for stochastic differential equations (SDEs) of jump-diffusion type. It provides first order strong approximations for jump-diffusion SDEs driven by Wiener processes and Poisson random measures. The paper covers first order derivative-free, drift-implicit and jump-adapted strong approximations. Moreover, it provides a commutativity condition under which the computational effort of first order strong schemes is independent of the total intensity of the jump measure. Finally, a numerical study on the accuracy of several strong schemes applied to the Merton model is presented. © VSP 2006.

Chiarella, C. & Nikitopoulos Sklibosios, C. 2003, 'A Class of Jump-Diffusion Bond Pricing Models within the HJM Framework',

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*Asia - Pacific Financial Markets*, vol. 10, no. 2-3, pp. 87-127.View/Download from: UTS OPUS

This paper considers a class of term structure models that is a parameterisation of the Shirakawa (1991) extension of the Heath et al. (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 distribution.

## Other

Chiarella, C., Nikitopoulos-Sklibosios, C., Schlogl, E. & Yang, H. 2016, 'Pricing American Options under Regime Switching Using Method of Lines'.

This paper considers the American option pricing problem under regime-switching by using the method-of-lines (MOL) scheme. American option prices in each regime involve prices
in all other regimes. We treat the prices from other regimes implicitly, thus guaranteeing consistency. Iterative procedures are required but very few iterative steps are needed in
practice. Numerical tests demonstrate the robustness, accuracy and efficiency of the proposed numerical scheme. We compare our results with Buffington and Elliott (2002)'s analytical
approximation under two regimes. Our MOL scheme provides improved results especially for out-of-the money options, possibly because they use a separation of variable approach to the PDEs
which cannot hold around the early exercise region. We also compare our results with those of Khaliq and Liu (2009) and suggest that their implicit scheme can be improved.

Cheng, B., Nikitopoulos-Sklibosios, C. & Schlogl, E. 2015, 'Pricing of Long-dated Commodity Derivatives with Stochastic Volatility and Stochastic Interest Rates'.

Aiming to study pricing of long-dated commodity derivatives, this paper presents a class of models within the Heath, Jarrow, and Morton (1992) framework for commodity futures
prices that incorporates stochastic volatility and stochastic interest rate and allows a correlation structure between the futures price process, the futures volatility process and the
interest rate process. The functional form of the futures price volatility is specified so that the model admits finite dimensional realisations and retains affine representations,
henceforth quasi-analytical European futures option pricing formulae can be obtained. A sensitivity analysis reveals that the correlation between the interest rate process and the futures
price process has noticeable impact on the prices of long-dated futures options, while the correlation between the interest rate process and the futures price volatility process does not
impact option prices. Furthermore, when interest rates are negatively correlated with futures prices then option prices are more sensitive to the volatility of interest rates, an effect
that is more pronounced with longer maturity options.

Chiarella, C., Maina, S.C. & Nikitopoulos Sklibosios, C. 2010, 'Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility',

*Research Paper Series, Quantitative Finance Research Centre, University of Technology, Sydney*. Research Paper Number: 283 <p>Abstract: This paper presents a class of defaultable term structure models within the HJM framework with stochastic volatility. Under certain volatility speci¬cations, the model admits ¬nite dimensional Markovian structures and consequently provides tractable solutions for defaultable bond prices. Furthermore, a bond pricing formula is obtained in terms of market observable quantities, speci¬cally in terms of discrete tenor forward rates. The effect of stochastic volatility and of correlations between the stochastic volatility, defaultable short rate and credit spreads on the defaultable bond prices and returns is also investigated.

Bruti Liberati, N., Nikitopoulos Sklibosios, C., Platen, E. & Schlogl, E. 2009, 'Alternative Defaultable Term Structure Models',

*Quantitative Finance Research Paper Series*. The objective of this paper is to consider defaultable term structure models in a general setting beyond standard risk-neutral models. Using as numeraire the growth optimal portfolio, defaultable interest rate derivatives are priced under the real-world probability measure. Therefore, the existence of an equivalent risk-neutral probability measure is not required. In particular, the real-world dynamics of the instantaneous defaultable forward rates under a jump-diffusion extension of a HJM type framework are derived. Thus, by establishing a modelling framework fully under the real-world probability measure, the challenge of reconciling real-world and risk-neutral probabilities of default is deliberately avoided, which provides significant extra modelling freedom. In addition, for certain volatility specifications, finite dimensional Markovian defaultable term structure models are derived. The paper also demonstrates an alternative defaultable term structure model. It provides tractable expressions for the prices of defaultable derivatives under the assumption of independence between the discounted growth optimal portfolio and the default-adjusted short rate. These expressions are then used in a more general model as control variates for Monte Carlo simulations of credit derivatives.

Bruti Liberati, N., Nikitopoulos Sklibosios, C. & Platen, E. 2007, 'Pricing Under the Real-World Probability Measure for Jump-Diffusion Term Structure Models',

*Quantitative Finance Research Paper Series*. This paper considers interest rate term structure models in a market attracting both continuous and discrete types of uncertainty. The event driven noise is modelled by a Poisson random measure. Using as numeraire the growth optimal portfolio, interest rate derivatives are priced under the real-world probability measure. In particular, the real-world dynamics of the forward rates are derived and, for specific volatility structures, finite dimensional Markovian representations are obtained. Furthermore, allowing for a stochastic short rate, a class of tractable affine term structures is derived where an equivalent risk-neutral probability measure does not exist.

Chiarella, C., Nikitopoulos Sklibosios, C. & Schlogl, E. 2005, 'A control variate method for Monte Carlo simulations of Heath-Jarrow-Morton with jumps (QFRC paper #167)'.

ISSN 1441-8010 www.business.uts.edu.au/qfrc/research/research_papers/rp167.pdf

Chiarella, C. & Nikitopoulos Sklibosios, C. 2004, 'A class of jump-diffusion bond pricing models within the HJM framework (QFRC paper #132)'.

Chiarella, C., Schlogl, E. & Nikitopoulos Sklibosios, C. 2004, 'A Markovian defaultable term structure model with state dependent volatilities (QFRC paper #135)'.

**Selected Peer-Assessed Projects**