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Dr Boda Kang

Biography

Boda joined UTS in March 2007 as a research associate working with Professor Carl Chiarella on a project of American option pricing after finishing his PhD in Financial Mathematics at the School of Mathematics and Statistics, University of South Australia. In 2004, during the second year of his PhD, he received a Chinese government award for outstanding self-financed PhD students abroad, including a certificate and US$5,000 to each winner. He is one of 14 Chinese PhD students studying in Australia to have received this award. Before coming to Australia, he finished his Bachelor of Science in Applied Mathematics and Master of Science in Probability and Mathematical Statistics both from Department of Mathematical Science, at Tsinghua University, Beijing, China. His research interests include financial derivatives pricing, dynamic value-at-risk (VaR) and conditional value-at-risk (CVaR) analysis, time consistent risk measures, risk analysis in both financial market and environmental problems, Markov decision processes and financial mathematics. He has published a couple of refereed papers in international journals and edited volumes. He has also presented his research on a number of national and international conferences.

Visiting Fellow, Finance Discipline Group
Associate Member, Quantitative Finance Research Centre
B.Sc(Tsinghua), M.Sc(Tsinghua), PhD(UniSA)
 
Can supervise: Yes

Books

Chiarella, C., Kang, B. & Meyer, G. 2014, The numerical solution of the American option pricing problem: Finite difference and transform approaches, 1st, World Scientific Publishing Co, USA.
Kang, B. 2008, Measures of Risk - Time Consistency and Surrogate Processes, VDM Verlag Dr. Muller, Germany.
This book is mainly based on my PhD thesis I completed in School of Mathematics and Statistics at University of South Australia, Adelaide 2006

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.
Filar, J. & Kang, B. 2006, 'Two Types of Risk' in Yan, H., Yin, G. & Zhang, Q. (eds), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queue, Springer, Germany, pp. 109-140.
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The risk encountered in many environmental problems appears to exhibit special two-sided characteristics. For instance, in a given area and in a given period, farmers do not want to see too much or too little rainfall. They hope for rainfall that is in some given interval. We formulate and solve this problem with the help of a two-sided loss function that depends on the above range. Even in financial portfolio optimization a loss and a gain are two sides of a coin, so it is desirable to deal with them in a manner that reflects an investors relative concern. Consequently, in this paper, we define Type I risk: the loss is too big and Type II risk: the gain is too small. Ideally, we would want to minimize the two risks simultaneously. However, this may be impossible and hence we try to balance these two kinds of risk. Namely, we tolerate certain amount of one risk when minimizing the other. The latter problem is formulated as a suitable optimization problem and illustrated with a numerical example.

Conferences

Chiarella, C., Griebsch, S. & Kang, B. 2014, 'A comparative study on time-efficient methods to price compound options in the Heston model'.
Chiarella, C., Kang, B., Nikitopoulos, C.S. & T, T.-.D. 2013, 'Humps in the volatility structure of the crude oil futures market: New evidence', Energy Economics, 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. 2013 Elsevier B.V.
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., Kang, B. & Meyer, G. 2013, 'The evaluation of barrier option prices under stochastic volatility'.
Chiarella, C., Kang, B. & Poon, S. 2013, 'Forward variance and VIX futures dynamics'.
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.
View/Download from: Publisher's site
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. 2012, 'The evaluation of gas swing contracts with regime switching', Topics in Numerical Methods for Finance: Proceedings in Mathematics and Statistics, Springer, Germany, pp. 155-176.
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Beyna, I., Chiarella, C. & Kang, B. 2012, 'Pricing interest rate derivatives in a multifactor HJM model with time dependent volatility'.
Chiarella, C. & Kang, B. 2012, 'The evaluation of American compound option prices under stochastic volatility and stochastic interest rates'.
Chiarella, C., Kang, B., Nikitopoulos Sklibosios, C. & To, T. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence'.
Chiarella, C., Kang, B. & Meyer, G. 2012, 'The evaluation of barrier option prices under stochastic volatility'.
Chiarella, C., Kang, B. & Nikitopoulos Sklibosios, C. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence'.
Chiarella, C., Kang, B. & Nikitopoulos Sklibosios, C. 2012, 'Humps in the volatility structure of the crude oil futures market: New evidence"'.
Chiarella, C. & Kang, B. 2011, 'The evaluation of American compound option prices under stochastic volatility and stochastic interest rates'.
Chiarella, C., Benya, I. & Kang, B. 2011, 'Pricing interest rate derivatives in a multifactor HJM model with time dependent volatility'.
Chiarella, C., Clewlow, L. & Kang, B. 2010, 'The evaluation of swing contracts with regime switching'.
Chiarella, C., Kang, B. & Meyer, G. 2010, 'The evaluation of barrier option prices under stochastic volatility'.
Chiarella, C., Clewlow, L. & Kang, B. 2010, 'Modelling and estimating the forward price curve in the energy market'.
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'.
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 Hestons 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'.
Chiarella, C., Clewlow, L. & Kang, B. 2009, 'Modelling and estimating the forward price curve in the energy market'.
Kang, B. 2008, 'The evaluation of American compound option prices under stochastic volatility'.
Chiarella, C., Clewlow, L. & Kang, B. 2008, 'The evaluation of swing option price with make-up and carry-forward provisions'.
Chiarella, C. & Kang, B. 2008, 'The evaluation of American compound option prices under stochastic volatility'.
Kang, B. 2006, 'Pricing financial derivatives on weather sensitive assets'.
Kang, B. 2005, 'Time consistent dynamic risk measures'.
Kang, B. 2004, 'Value-at-risk, two sided version'.

Journal articles

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., 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.
View/Download from: 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. & 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.
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., 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.
View/Download from: Publisher's site
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.
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.
Kang, B. & Filar, J. 2006, 'Time consistent dynamic risk measures', Mathematical Methods of Operations Research, vol. 63, no. 1, pp. 169-186.
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We introduce the time-consistency concept that is inspired by the so-called principle of optimality of dynamic programming and demonstrate via an example that the conditional value-at-risk (CVaR) need not be time-consistent in a multi-stage case. Then, we give the formulation of the target-percentile risk measure which is time-consistent and hence more suitable in the multi-stage investment context. Finally, we also generalize the value-at-risk and CVaR to multi-stage risk measures based on the theory and structure of the target-percentile risk measure.
Kang, B., Filar, J., Lin, Y. & Spanjers, L. 2004, 'Stochastic Target Hitting Time and the Problem of Early Retirement', IEEE Transactions On Automatic Control, vol. 49, no. 3, pp. 409-419.
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We consider a problem of optimal control of a retirement investment fund over a finite time horizon with a target hitting time criteria. That is, we wish to decide, at each stage, what percentage of the current retirement fund to allocate into the limited number of investment options so that a decision maker can maximize the probability that his or her wealth exceeds a target prior to his or her retirement. We use Markov decision processes with probability criteria to model this problem and give an example based on data from certain options available in an Australian retirement fund.
Lin, Y., Wu, C. & Kang, B. 2003, 'Optimal Models with Maximizing the Probability of First Achieving Target Value in the Preceding Stages', Science In China Series A, vol. 46, no. 3, pp. 396-414.
Decision makers often face the need of performance guarantee with some sufficiently high probability. Such problems can be modelled using a discrete time Markov decision process (MDP) with a probability criterion for the first achieving target value. The objective is to find a policy that maximizes the probability of the total discounted reward exceeding a target value in the preceding stages. We show that our formulation cannot be described by former models with standard criteria. We provide the properties of the objective functions, optimal value functions and optimal policies. An algorithm for computing the optimal policies for the finite horizon case is given. In this stochastic stopping model, we prove that there exists an optimal deterministic and stationary policy and the optimality equation has a unique solution. Using perturbation analysis, we approximate general models and prove the existence of ?-optimal policy for finite state space. We give an example for the reliability of the satellite systems using the above theory. Finally, we extend these results to more general cases.
Lin, Y., Kang, B. & Wu, C. 2001, 'Finite horizon markov decision minimizing risk Models in borel state space', Chinese Sciences Abstract Series A, vol. ?, pp. 1273-1278.
Lin, Y., Wu, C. & Kang, B. 2001, 'Markov decision minimizing risk models for the first achieving target value', Chinese Sciences Abstract Series A, vol. ?, pp. 1269-1273.

Other

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. & 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 Hestons 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 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 regimes witching and seasonality. Applications to the market gas forward data shows that the MCMC approach provides stable estimates.
Filar, J., Kang, B. & Korolkiewicz, M. 2008, 'Pricing Financial Derivatives on Weather Sensitive Assets (223)', Quantitative Finance Research Paper Series.
We study pricing of derivatives when the underlying asset is sensitive to weather variables such as temperature, rainfall and others. We shall use temperature as a generic example of an important weather variable. In reality, such a variable would only account for a portion of the variability in the price of an asset. However, for the purpose of launching this line of investigations we shall assume that the asset price is a deterministic function of temperature and consider two functional forms: quadratic and exponential. We use the simplest mean-reverting process to model the temperature, the AR(1) time series model and its continuous-time counterpart the Ornstein-Uhlenbeck process. In continuous time, we use the replicating portfolio approach to obtain partial differential equations for a European call option price under both functional forms of the relationship between the weather-sensitive asset price and temperature. For the continuous-time model we also derive a binomial approximation, a finite difference method and a Monte Carlo simulation to numerically solve our option price PDE. In the discrete time model, we derive the distribution of the underlying asset and a formula for the value of a European call option under the physical probability measure.