Pricing forward starting options under regime switching jump diffusion models

Abstract: This paper studies the pricing of forward starting options under regime switching jump diffusion models. We suppose that a market economy has only two states, one is a stable state, the other is a high volatility state. The dynamics of a risky asset is modeled by a geometry Brownian motion when the market state is stable, otherwise, it follows a jump diffusion model. We propose two types of regime switching jump diffusion models: one is a two-state regime switching Merton jump diffusion model, and the other is a two-state regime switching double exponential jump diffusion model. Finally, some analytic formulas for pricing forward starting options are derived under these regime switching jump diffusion models.