Journal of Computational and Applied Mathematics
Traffic generated by a semi-markov additive process
Probability in the Engineering and Informational Sciences
First passage of time-reversible spectrally negative Markov additive processes
Operations Research Letters
Asymptotic analysis of option pricing in a Markov modulated market
Operations Research Letters
Journal of Computational and Applied Mathematics
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Markov-modulated models for equity prices have recently been extensively studied in the literature. In this paper, we apply some old results on the Wiener--Hopf factorization of Markov processes to a range of option-pricing problems for such models. The first example is the perpetual American put, where the exact (numerical) solution is obtained without discretizing any PDE. We then show how the methodology of Rogers and Stapleton [Finance Stoch., 2 (1997), pp. 3-17] can be used to tackle finite-horizon problems and illustrate the methodology by pricing European, American, single barrier, and double barrier options under Markov-modulated dynamics.