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Regime-Switching Risk: To Price or Not to Price?

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  • Tak Kuen Siu

Abstract

Should the regime-switching risk be priced? This is perhaps one of the important “normative” issues to be addressed in pricing contingent claims under a Markovian, regime-switching, Black-Scholes-Merton model. We address this issue using a minimal relative entropy approach. Firstly, we apply a martingale representation for a double martingale to characterize the canonical space of equivalent martingale measures which may be viewed as the largest space of equivalent martingale measures to incorporate both the diffusion risk and the regime-switching risk. Then we show that an optimal equivalent martingale measure over the canonical space selected by minimizing the relative entropy between an equivalent martingale measure and the real-world probability measure does not price the regime-switching risk. The optimal measure also justifies the use of the Esscher transform for option valuation in the regime-switching market.

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  • Tak Kuen Siu, 2011. "Regime-Switching Risk: To Price or Not to Price?," International Journal of Stochastic Analysis, Hindawi, vol. 2011, pages 1-14, December.
    • Handle: RePEc:hin:jnijsa:843246
    DOI: 10.1155/2011/843246
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    Cited by:

    1. David Liu, 2020. "Markov modulated jump-diffusions for currency options when regime switching risk is priced," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 1-26, February.

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