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Option pricing when the regime-switching risk is priced

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Abstract

We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion. We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time, finite-state Markov chain. We develop a two-stage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states. Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Curtin University of Technology, Perth, W.A., 6845, Australia

    Tak Kuen Siu

  2. Department of Statistics and Actuarial Science, the University of Hong Kong, Pokfulam Road, Hong Kong, China

    Hailiang Yang

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  1. Tak Kuen Siu
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  2. Hailiang Yang
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Correspondence to Hailiang Yang.

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Siu, T.K., Yang, H. Option pricing when the regime-switching risk is priced. Acta Math. Appl. Sin. Engl. Ser. 25, 369–388 (2009). https://doi.org/10.1007/s10255-008-8803-5

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  • DOI: https://doi.org/10.1007/s10255-008-8803-5

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