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Option Pricing in a Jump-Diffusion Model with Regime Switching

Published online by Cambridge University Press:  09 August 2013

Fei Lung Yuen  and
Hailiang Yang
Fei Lung Yuen
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong
Hailiang Yang
Affiliation:
Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong
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Abstract

Nowadays, the regime switching model has become a popular model in mathematical finance and actuarial science. The market is not complete when the model has regime switching. Thus, pricing the regime switching risk is an important issue. In Naik (1993), a jump diffusion model with two regimes is studied. In this paper, we extend the model of Naik (1993) to a multi-regime case. We present a trinomial tree method to price options in the extended model. Our results show that the trinomial tree method in this paper is an effective method; it is very fast and easy to implement. Compared with the existing methodologies, the proposed method has an obvious advantage when one needs to price exotic options and the number of regime states is large. Various numerical examples are presented to illustrate the ideas and methodologies.

Keywords

Jump-diffusion modelTrinomial tree methodRegime switchingOption pricingPrice of regime switching risk
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 39 , Issue 2 , November 2009 , pp. 515 - 539
Copyright
Copyright © International Actuarial Association 2009

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References

Aingwirth, D.D., Das, S.R. and Motwani, R. (2006) A simple approach for pricing equity options with Markov switching state variables, Quantitative Finance, 6(2), 95–105.CrossRefGoogle Scholar
Baule, R. and Wilkens, M. (2004) Lean trees – a general approach for improving performance of lattice models for option pricing, Review of Derivatives Research, 7, 53–72.CrossRefGoogle Scholar
Black, F. and Scholes, M. (1973) The pricing of options and corporate liabilities, Journal of Political Economy, 81, 637–654.Google Scholar
Bollen, N.P.B. (1998) Valuing options in regime-switching models, Journal of Derivatives, 6, 8–49.Google Scholar
Boyle, P.P. (1986) Option valuation using a three-jump process, International Options Journal, 3, 7–12.Google Scholar
Boyle, P.P. (1988) A lattice framework for option pricing with two state variables, Journal of Financial and Quantitative Analysis, 23(1), 1–12.CrossRefGoogle Scholar
Boyle, P.P. and Draviam, T. (2007) Pricing exotic options under regime switching, Insurance: Mathematics and Economics, 40, 267–282.Google Scholar
Boyle, P.P. and Tian, Y. (1998) An explicit finite difference approach to the pricing of barrier options, Applied Mathematical Finance, 5, 17–43.CrossRefGoogle Scholar
Buffington, J. and Elliott, R.J. (2002) American options with regime switching, International Journal of Theoretical and Applied Finance, 5(5), 497–514.CrossRefGoogle Scholar
Cox, J.C., Ross, S.A. and Rubinstein, M. (1979) Option pricing: a simplified approach, Journal of Financial Economics, 7, 229–263.Google Scholar
Elliott, R.J., Chan, L.L. and Siu, T.K. (2005) Option pricing and Esscher transform under regime switching, Annals of Finance, 1, 423–432.Google Scholar
Elliott, R.J., Siu, T.K. and Lau, J.W. (2007) Pricing Options Under a Generalized Markov Modulated Jump Diffusion Model, Stochastic Analysis and Applications, 25(4), 821–843.Google Scholar
Figlewski, S. and Gao, B. (1999) The adaptive mesh model: a new approach to efficient option pricing, Journal of Financial Economics, 53, 313–351.CrossRefGoogle Scholar
Guo, X. (2001) Information and option pricings, Quantitative Finance, 1, 37–57.Google Scholar
Jarrow, R. and Rudd, A. (1983) Option Pricing, Dow Jones-Irwin, Homewood, Ill.Google Scholar
Kamrad, B. and Ritchken, P. (1991) Multinomial approximating models for options with k state variables, Management Science, 37(12), 1640–1652.Google Scholar
Merton, R.C. (1973) Theory of rational option pricing, Bell J. Econom. Manag. Sci., 4, 141–183.CrossRefGoogle Scholar
Merton, R.C. (1990) Continuous-Time Finance, Blackwell Publishers Inc., United Kingdom.Google Scholar
Momon, R.S. and Rodrigo, M.R. (2005) Explicit solutions to European options in a regime-switching economy, Operations Research Letters, 33, 581–586.Google Scholar
Naik, V. (1993) Option valuation and hedging strategies with jumps in volatility of asset returns, The Journal of Finance, 48(5), 1969–1984.Google Scholar
Omberg, E. (1987) A note on the convergence of binomial-pricing and compound-option models, The Journal of Finance, 42(2), 463–469.Google Scholar
Siu, T.K. (2008) A Game Theoretic Approach to Option Valuation Under Markovian Regime-Switching Models, Insurance: Mathematics and Economics, 42(3), 1146–1158.Google Scholar
Siu, T.K., Yang, H., Lau, J.W. (2008) Pricing Currency Options Under Two-Factor Markov-Modulated Stochastic Volatility Models, Insurance: Mathematics and Economics, 43(3), 295–302.Google Scholar