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Saddlepoint approximations to option price in a regime-switching model

Author

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  • Mengzhe Zhang

    (University of New South Wales)

  • Leunglung Chan

    (University of New South Wales)

Abstract

In this paper we consider the saddlepoint approximation for the valuation of a European-style call option in a Markovian, regime-switching, Black–Scholes–Merton economy, where the price process of an underlying risky asset is assumed to follow a Markov-modulated geometric Brownian motion. The standard option pricing procedure under this model becomes problematic as the occupation time of chains for a given state cannot be evaluated easily. In the case of two-state Markov chains, we present an explicit analytic formula of the cumulant generating function (CGF). When the process has more than two states, an approximate formula of the CGF is provided. We adopt a splitting method to reduce the complexity of computing the matrix exponential function. Then we use these CGFs to develop the use of the saddlepoint approximations. The numerical results show that the saddlepoint approximation is an efficient and reliable approach for option pricing under a multi-state regime-switching model.

Suggested Citation

  • Mengzhe Zhang & Leunglung Chan, 2016. "Saddlepoint approximations to option price in a regime-switching model," Annals of Finance, Springer, vol. 12(1), pages 55-69, February.
    • Handle: RePEc:kap:annfin:v:12:y:2016:i:1:d:10.1007_s10436-015-0272-2
    DOI: 10.1007/s10436-015-0272-2
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    References listed on IDEAS

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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Call option; Markov-modulated geometric Brownian motion; Regime switching model; Saddlepoint method;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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