A path-independent method for barrier option pricing in hidden Markov models

• We propose a path-independent method for pricing barrier options.
• We conduct an empirical study on barrier option pricing.
• We show that the proposed method is faster than Monte-Carlo simulation methods.

This paper presents a method for barrier option pricing under a Black–Scholes model with Markov switching. We extend the option pricing method of Buffington and Elliott to price continuously monitored barrier options under a Black–Scholes model with regime switching. We use a regime switching random Esscher transform in order to determine an equivalent martingale pricing measure, and then solve the resulting multidimensional integral for pricing barrier options. We have calculated prices for down-and-out call options under a two-state hidden Markov model using two different Monte-Carlo simulation approaches and the proposed method. A comparison of the results shows that our method is faster than Monte-Carlo simulation methods.