Pricing exotic options under regime switching

This paper studies the pricing of options when the volatility of the underlying asset depends upon a hidden Markov process which takes discrete values. It is assumed that the regime switching process is generated by time-independent rate parameters and is independent of the Brownian motion. We derive the coupled Black-Scholes-type partial differential equations that govern the dynamics of several exotic options. These include European, Asian and lookback options. The difference in option prices with and without regime switching is substantial for lookback options and more moderate for European and Asian options.