Option Pricing when the Regime-Switching Risk is Priced

We study the pricing of an option when the price dynamic of the underlying risky asset is governed by a Markov-modulated geometric Brownian motion.We suppose that the drift and volatility of the underlying risky asset are modulated by an observable continuous-time,finite-state Markov chain.We develop a twostage pricing model which can price both the diffusion risk and the regime-switching risk based on the Esscher transform and the minimization of the maximum entropy between an equivalent martingale measure and the real-world probability measure over different states.Numerical experiments are conducted and their results reveal that the impact of pricing regime-switching risk on the option prices is significant.