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Option Pricing in a Jump-Diffusion Model with Regime Switching

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  • Yuen, Fei Lung
  • Yang, Hailiang

Abstract

Nowadays, the regime switching model has become a popular model in mathematical finance and actuarial science. The market is not complete when the model has regime switching. Thus, pricing the regime switching risk is an important issue. In Naik (1993), a jump diffusion model with two regimes is studied. In this paper, we extend the model of Naik (1993) to a multi-regime case. We present a trinomial tree method to price options in the extended model. Our results show that the trinomial tree method in this paper is an effective method; it is very fast and easy to implement. Compared with the existing methodologies, the proposed method has an obvious advantage when one needs to price exotic options and the number of regime states is large. Various numerical examples are presented to illustrate the ideas and methodologies.

Suggested Citation

  • Yuen, Fei Lung & Yang, Hailiang, 2009. "Option Pricing in a Jump-Diffusion Model with Regime Switching," ASTIN Bulletin, Cambridge University Press, vol. 39(2), pages 515-539, November.
    • Handle: RePEc:cup:astinb:v:39:y:2009:i:02:p:515-539_00
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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. Pelsser, Antoon & Salahnejhad Ghalehjooghi, Ahmad, 2016. "Time-consistent actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 97-112.
    3. Adam W. Kolkiewicz & Fangyuan Sally Lin, 2017. "Pricing Surrender Risk in Ratchet Equity-Index Annuities under Regime-Switching Lévy Processes," North American Actuarial Journal, Taylor & Francis Journals, vol. 21(3), pages 433-457, July.
    4. Godin, Frédéric & Lai, Van Son & Trottier, Denis-Alexandre, 2019. "Option pricing under regime-switching models: Novel approaches removing path-dependence," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 130-142.
    5. Milan Kumar Das & Anindya Goswami, 2018. "Testing of Binary Regime Switching Models using Squeeze Duration Analysis," Papers 1807.04393, arXiv.org, revised Aug 2018.
    6. Tak Kuen Siu & Robert J. Elliott, 2019. "Hedging Options In A Doubly Markov-Modulated Financial Market Via Stochastic Flows," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(08), pages 1-41, December.
    7. Leunglung Chan & Song-Ping Zhu, 2014. "An exact and explicit formula for pricing Asian options with regime switching," Papers 1407.5091, arXiv.org.
    8. 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.
    9. J. Lars Kirkby & Duy Nguyen, 2020. "Efficient Asian option pricing under regime switching jump diffusions and stochastic volatility models," Annals of Finance, Springer, vol. 16(3), pages 307-351, September.
    10. 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.
    11. 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.
    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. Arunangshu Biswas & Anindya Goswami & Ludger Overbeck, 2017. "Option Pricing in a Regime Switching Stochastic Volatility Model," Papers 1707.01237, arXiv.org, revised Jan 2018.
    14. 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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