Option Pricing With Markov-Modulated Dynamics

Abstract

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.