Saddlepoint approximations to option price in a regime-switching model

Mengzhe Zhang () and Leunglung Chan ()
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Mengzhe Zhang: University of New South Wales
Leunglung Chan: University of New South Wales

Annals of Finance, 2016, vol. 12, issue 1, No 4, 55-69

Abstract: 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.

Keywords: Call option; Markov-modulated geometric Brownian motion; Regime switching model; Saddlepoint method (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10436-015-0272-2

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