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Option Valuation Under a Double Regime‐Switching Model

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  • Yang Shen
  • Kun Fan
  • Tak Kuen Siu

Abstract

This paper is concerned with option valuation under a double regime‐switching model, where both the model parameters and the price level of the risky share depend on a continuous‐time, finite‐state, observable Markov chain. In this incomplete market set up, we first employ a generalized version of the regime‐switching Esscher transform to select an equivalent martingale measure which can incorporate both the diffusion and regime‐switching risks. Using an inverse Fourier transform, an analytical option pricing formula is obtained. Finally, we apply the fast Fourier transform method to compute option prices. Numerical examples and empirical studies are used to illustrate the practical implementation of our method. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:451–478, 2014

Suggested Citation

  • Yang Shen & Kun Fan & Tak Kuen Siu, 2014. "Option Valuation Under a Double Regime‐Switching Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(5), pages 451-478, May.
    • Handle: RePEc:wly:jfutmk:v:34:y:2014:i:5:p:451-478
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    Cited by:

    1. Colwell, David B., 2023. "Hitting times, number of jumps, and occupation times for continuous-time finite state Markov chains," Statistics & Probability Letters, Elsevier, vol. 195(C).
    2. Ignatieva, Katja & Song, Andrew & Ziveyi, Jonathan, 2016. "Pricing and hedging of guaranteed minimum benefits under regime-switching and stochastic mortality," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 286-300.
    3. Wenlong Hu, 2020. "Risk management of guaranteed minimum maturity benefits under stochastic mortality and regime-switching by Fourier space time-stepping framework," Papers 2006.15483, arXiv.org, revised Dec 2020.
    4. 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.
    5. Donatien Hainaut & Franck Moraux, 2019. "A switching self-exciting jump diffusion process for stock prices," Annals of Finance, Springer, vol. 15(2), pages 267-306, June.
    6. Mehrdoust, Farshid & Noorani, Idin & Hamdi, Abdelouahed, 2023. "Two-factor Heston model equipped with regime-switching: American option pricing and model calibration by Levenberg–Marquardt optimization algorithm," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 660-678.
    7. Chen Tong & Peter Reinhard Hansen & Zhuo Huang, 2022. "Option pricing with state‐dependent pricing kernel," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 42(8), pages 1409-1433, August.
    8. Jung Ho Park & Kwangsoo Shin, 2018. "R&D Project Valuation Considering Changes of Economic Environment: A Case of a Pharmaceutical R&D Project," Sustainability, MDPI, vol. 10(4), pages 1-15, March.
    9. Siu, Tak Kuen, 2023. "European option pricing with market frictions, regime switches and model uncertainty," Insurance: Mathematics and Economics, Elsevier, vol. 113(C), pages 233-250.
    10. Mehrdoust, Farshid & Noorani, Idin & Kanniainen, Juho, 2024. "Valuation of option price in commodity markets described by a Markov-switching model: A case study of WTI crude oil market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 228-269.
    11. Forsyth, Peter & Vetzal, Kenneth, 2014. "An optimal stochastic control framework for determining the cost of hedging of variable annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 29-53.
    12. Fan, Kun & Shen, Yang & Siu, Tak Kuen & Wang, Rongming, 2015. "Valuing commodity options and futures options with changing economic conditions," Economic Modelling, Elsevier, vol. 51(C), pages 524-533.
    13. 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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