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Risk-minimizing option pricing under a Markov-modulated jump-diffusion model with stochastic volatility

  • Su, Xiaonan
  • Wang, Wensheng
  • Hwang, Kyo-Shin
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    In this paper, we deal with the pricing of European style options when the dynamics of the risky underlying asset are driven by a Markov-modulated jump diffusion with stochastic volatility. We investigate the Radon–Nikodym derivative for the minimal martingale measure and a partial differential equation approach for pricing European options. An optimal hedging strategy in terms of local risk minimization is obtained.

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    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 82 (2012)
    Issue (Month): 10 ()
    Pages: 1777-1785

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    Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1777-1785
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    1. 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.
    2. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    3. Rüdiger Frey, 2000. "Risk Minimization with Incomplete Information in a Model for High-Frequency Data," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 215-225.
    4. Kiseop Lee & Seongjoo Song, 2007. "Insiders' hedging in a jump diffusion model," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 537-545.
    5. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    6. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    7. Siu, Tak Kuen & Yang, Hailiang & Lau, John W., 2008. "Pricing currency options under two-factor Markov-modulated stochastic volatility models," Insurance: Mathematics and Economics, Elsevier, vol. 43(3), pages 295-302, December.
    8. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
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