A Lattice Method for Lookback Options with Regime-Switching Volatility

Abstract

We develop a lattice method for pricing lookback options in a regime-switching market environment. We assume the market is governed by a two-state Markov chain and stock volatility can change whenever the market environment changes. We develop a method which resolves the bias in the binomial method of Babbs (2000), and combine it with the pentanomial method of Bollen (1998). Our method can be used for American-style lookback options as well as European-style lookback options and is a simple but efficient way for pricing them compared with the methods currently available. We also analyze the convergence of the proposed method.