Option Pricing with a Regime-Switching Levy Model

In this paper, we present analytical solutions for the Laplace transforms of vanilla, barrier, and lookback options when the underlying process is a regime-switching jump-diffusion process. These closed-form solutions are possible due to the analytical characterization of the joint distribution of the underlying process with its running maximum or minimum under the regime-switching jump-diffusion model, developed in Kijima and Siu (2010). By performing the appropriate numerical Laplace inversion, we can recover the corresponding prices efficiently and stably.