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Option pricing with Markov-modulated dynamics. (English) Zbl 1158.91380
Summary: 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 L. C. G. Rogers and E. J. Stapleton [Finance Stoch. 2, No. 1, 3–17 (1998; Zbl 0894.90025)] 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.
MSC:
91B28Finance etc. (MSC2000)
60H10Stochastic ordinary differential equations
60H30Applications of stochastic analysis
93E20Optimal stochastic control (systems)