In this paper we consider a jump-diffusion dynamic whose parameters are driven by a\udcontinuous time and stationary Markov Chain on a finite state space as a model for the\udunderlying 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\udresults 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.
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