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A risk-based approach for pricing American options under a generalized Markov regime-switching model

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  • Robert Elliott
  • Tak Siu

Abstract

This paper considers a risk-based approach for pricing an American contingent claim in an incomplete market described by a continuous-time, Markov, regime-switching jump-diffusion model. We formulate the valuation problem as a stochastic differential game and use dynamic programming. Verification theorems for the Hamilton–Jacobi–Bellman–Issacs (HJBI) variational inequalities of the games are used to determine the seller's and buyer's prices and optimal exercise strategies.

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  • Robert Elliott & Tak Siu, 2011. "A risk-based approach for pricing American options under a generalized Markov regime-switching model," Quantitative Finance, Taylor & Francis Journals, vol. 11(11), pages 1633-1646.
    • Handle: RePEc:taf:quantf:v:11:y:2011:i:11:p:1633-1646
    DOI: 10.1080/14697688.2011.615215
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    Cited by:

    1. Lian, Yu-Min & Liao, Szu-Lang & Chen, Jun-Home, 2015. "State-dependent jump risks for American gold futures option pricing," The North American Journal of Economics and Finance, Elsevier, vol. 33(C), pages 115-133.
    2. Chang, Charles & Fuh, Cheng-Der & Lin, Shih-Kuei, 2013. "A tale of two regimes: Theory and empirical evidence for a Markov-modulated jump diffusion model of equity returns and derivative pricing implications," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3204-3217.
    3. 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.
    4. 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.
    5. Ehsan Hajizadeh & Masoud Mahootchi, 2019. "Developing a Risk-Based Approach for American Basket Option Pricing," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1593-1612, April.
    6. Haixiang Yao & Xun Li & Zhifeng Hao & Yong Li, 2016. "Dynamic asset–liability management in a Markov market with stochastic cash flows," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1575-1597, October.
    7. Siu, Tak Kuen, 2016. "A self-exciting threshold jump–diffusion model for option valuation," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 168-193.

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