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Stochastic Optimization Algorithms for Pricing American Put Options Under Regime-Switching Models

Author

Listed:
  • G. Yin

    (Wayne State University)

  • J. W. Wang

    (CitiGroup Inc.)

  • Q. Zhang

    (University of Georgia)

  • Y. J. Liu

    (Missouri Southern State University)

Abstract

This work provides a Markov-modulated stochastic approximation based approach for pricing American put options under a regime-switching geometric Brownian motion market model. The solutions of pricing American options may be characterized by certain threshold values. Here, a class of Markov-modulated stochastic approximation (SA) algorithms is developed to determine the optimal threshold levels. For option pricing in a finite horizon, a SA procedure is carried out for a fixed time T. As T varies, the optimal threshold values obtained via SA trace out a curve, called the threshold frontier. Numerical experiments are reported to demonstrate the effectiveness of the approach. Our approach provides us with a viable computational tool and has advantage in terms of the reduced computational complexity compared with the variational or quasivariational inequality methods for optimal stopping.

Suggested Citation

  • G. Yin & J. W. Wang & Q. Zhang & Y. J. Liu, 2006. "Stochastic Optimization Algorithms for Pricing American Put Options Under Regime-Switching Models," Journal of Optimization Theory and Applications, Springer, vol. 131(1), pages 37-52, October.
    • Handle: RePEc:spr:joptap:v:131:y:2006:i:1:d:10.1007_s10957-006-9134-4
    DOI: 10.1007/s10957-006-9134-4
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    References listed on IDEAS

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    1. John Buffington & Robert J. Elliott, 2002. "American Options With Regime Switching," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 497-514.
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    Cited by:

    1. 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.
    2. Takayuki Wada & Yasumasa Fujisaki, 2016. "Stopping Rules for Optimization Algorithms Based on Stochastic Approximation," Journal of Optimization Theory and Applications, Springer, vol. 169(2), pages 568-586, May.

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