  In this paper we consider a jump-diffusion dynamic whose parameters are
driven by a continuous time and stationary Markov Chain on a finite state space
as a model for the underlying of European contingent claims. For this class of
processes we firstly outline the Fourier transform method both in log-price and
log-strike to efficiently calculate the value of various types of options and
as a concrete example of application, we present some numerical results within
a two-state regime switching version of the Merton jump-diffusion model. Then
we develop a closed-form solution to the problem of pricing a Forward Starting
Option and use this result to approximate the value of such a derivative in a
general stochastic volatility framework.
