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

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  • Su, Xiaonan
  • Wang, Wensheng
  • Hwang, Kyo-Shin

Abstract

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.

Suggested Citation

  • Su, Xiaonan & Wang, Wensheng & Hwang, Kyo-Shin, 2012. "Risk-minimizing option pricing under a Markov-modulated jump-diffusion model with stochastic volatility," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1777-1785.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1777-1785
    DOI: 10.1016/j.spl.2012.05.026
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    References listed on IDEAS

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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. 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.
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    5. 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, April.
    6. Schweizer, Martin, 1991. "Option hedging for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 37(2), pages 339-363, April.
    7. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    8. Kiseop Lee & Seongjoo Song, 2007. "Insiders' hedging in a jump diffusion model," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 537-545.
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    Citations

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    Cited by:

    1. Milan Kumar Das & Anindya Goswami, 2019. "Testing of binary regime switching models using squeeze duration analysis," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-20, March.
    2. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Pricing annuity guarantees under a double regime-switching model," Insurance: Mathematics and Economics, Elsevier, vol. 62(C), pages 62-78.
    3. Milan Kumar Das & Anindya Goswami, 2018. "Testing of Binary Regime Switching Models using Squeeze Duration Analysis," Papers 1807.04393, arXiv.org, revised Aug 2018.
    4. Anindya Goswami & Omkar Manjarekar & Anjana R, 2018. "Option Pricing in a Regime Switching Jump Diffusion Model," Papers 1811.11379, arXiv.org, revised Oct 2019.
    5. Biswas, Arunangshu & Goswami, Anindya & Overbeck, Ludger, 2018. "Option pricing in a regime switching stochastic volatility model," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 116-126.
    6. Anindya Goswami & Kedar Nath Mukherjee & Irvine Homi Patalwala & Sanjay N. S, 2022. "Regime recovery using implied volatility in Markov modulated market model," Papers 2201.10304, arXiv.org, revised Mar 2022.
    7. Elham Dastranj & Roghaye Latifi, 2017. "A comparison of option pricing models," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(02n03), pages 1-11, June.

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