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Gibbs sampler with jump diffusion model: application in European call option and annuity

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  • Kein Joe Lau
  • Yong Kheng Goh
  • An-Chow Lai

Abstract

In this paper, we are presenting a method for estimation of market parameters modeled by jump diffusion process. The method proposed is based on Gibbs sampler, while the market parameters are the drift, the volatility, the jump intensity and its rate of occurrence. Demonstration on how to use these parameters to estimate the fair price of European call option and annuity will be shown, for the situation where the market is modeled by jump diffusion process with different intensity and occurrence. The results is compared to conventional options to observe the impact of jump effects.

Suggested Citation

  • Kein Joe Lau & Yong Kheng Goh & An-Chow Lai, 2017. "Gibbs sampler with jump diffusion model: application in European call option and annuity," Papers 1712.07796, arXiv.org.
    • Handle: RePEc:arx:papers:1712.07796
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    References listed on IDEAS

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    1. S. James Press, 1967. "A Compound Events Model for Security Prices," The Journal of Business, University of Chicago Press, vol. 40, pages 317-317.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    3. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    4. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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