Russian and American put options under exponential phase-type Levy models

Consider the American put and Russian option (Ann. Appl. Probab. 3 (1993) 603; Theory Probab. Appl. 39 (1994) 103; Ann. Appl. Probab. 3 (1993) 641) with the stock price modeled as an exponential Levy process. We find an explicit expression for the price in the dense class of Levy processes with phase-type jumps in both directions. The solution rests on the reduction to the first passage time problem for (reflected) Levy 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 Levy processes with phase-type jumps. (C) 2003 Published by Elsevier B.V.