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.