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Russian and American put options under exponential phase-type Lévy models. (English) Zbl 1075.60037

Summary: Consider the American put and Russian option with the stock price modeled as an exponential Lévy process. We find an explicit expression for the price in the dense class of Lévy processes with phase-type jumps in both directions. The solution rests on the reduction to the first passage time problem for (reflected) Lévy processes and on an explicit solution of the latter in the phase-type case via martingale stopping and Wiener-Hopf factorization. The same type of approach is also applied to the more general class of regime switching Lévy processes with phase-type jumps.

MSC:

60G40 Stopping times; optimal stopping problems; gambling theory
91B28 Finance etc. (MSC2000)

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