MPS-RR 2002-23
June 2002

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

Søren Asmussen

Florin Avram, Martijn R. Pistorius

Abstract

Consider the American put and Russian option [33, 34, 17] 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 factorisation. Also the first passage time problem is studied for a regime switching Lévy process with phase-type jumps. This is achieved by an embedding into a semi-Markovian regime switching Brownian motion.

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