Pricing Forward Starting Call Options under a Markov-Modulated Jump Diffusion Process

The pricing problem of forward starting call options under aMarkov-modulated jump diffusion process is studied. Under the assumption that the dynamics of risky asset follows a Markov-modulated jump diffusion process, the explicit analytical formula of forward starting call options is obtained by the change of measure and no arbitrage pricing theory. Moreover, the numerical results of option value are provided by the Monte Carlo method, and the value of forward starting call options is compared when the risky asset satisfies different financial models.