Option Pricing with Markov Switching

Abstract

In this article, we consider a model of time-varying volatility which generalizes the classical Black-Scholes model to include regime-switching properties. Specically, the unobservable state variables for stock uctu- ations are modeled by a Markov process, and the drift and volatility pa- rameters take dierent values depending on the state of this hidden Markov process. We provide a closed-form formula for the arbitrage-free price of the European call option, when the hidden Markov process has nite number of states. Two simulation methods, the discrete diusion method and the Markovian tree method, for computing the European call option price are presented for comparison.