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Saddlepoint Method for Pricing European Options under Markov-Switching Heston’s Stochastic Volatility Model

Author

Listed:
  • Mengzhe Zhang

    (Psychometrics and Analytics Branch, NSW Education Standards Authority, Sydney, NSW 2001, Australia)

  • Leunglung Chan

    (School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia)

Abstract

This paper evaluates the prices of European-style options when dynamics of the underlying asset is assumed to follow a Markov-switching Heston’s stochastic volatility model. Under this framework, the expected return and the long-term mean of the variance of the underlying asset rely on states of the economy modeled by a continuous-time Markov chain. There is evidence that the Markov-switching Heston’s stochastic volatility model performs well in capturing major events affecting price dynamics. However, due to the nature of the model, analytic solutions for the prices of options or other financial derivatives do not exist. By means of the saddlepoint method, an analytic approximation for European-style option price is presented. The saddlepoint method gives an effective approximation to option prices under the Markov-switching Heston’s stochastic volatility model.

Suggested Citation

  • Mengzhe Zhang & Leunglung Chan, 2022. "Saddlepoint Method for Pricing European Options under Markov-Switching Heston’s Stochastic Volatility Model," JRFM, MDPI, vol. 15(9), pages 1-9, September.
    • Handle: RePEc:gam:jjrfmx:v:15:y:2022:i:9:p:396-:d:908264
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    References listed on IDEAS

    as
    1. Boyle, Phelim & Draviam, Thangaraj, 2007. "Pricing exotic options under regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 40(2), pages 267-282, March.
    2. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    3. Glasserman, Paul & Kim, Kyoung-Kuk, 2009. "Saddlepoint approximations for affine jump-diffusion models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 15-36, January.
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