An exact and explicit formula for pricing lookback options with regime switching

TL;DR

This paper derives an exact, explicit formula for pricing European lookback options in a regime-switching model where asset dynamics depend on an unobservable Markov chain, enhancing accuracy in complex market conditions.

Contribution

It provides the first closed-form solution for lookback options under a two-state regime switching model, accounting for unobservable economic states.

Findings

Explicit formula for lookback options in regime switching models

Applicable to two-state Markov-modulated geometric Brownian motion

Enhances pricing accuracy in changing economic environments

Abstract

This paper investigates the pricing of European-style lookback options when the price dynamics of the underlying risky asset are assumed to follow a Markov-modulated Geo-metric Brownian motion; that is, the appreciation rate and the volatility of the underlying risky asset depend on unobservable states of the economy described by a continuous-time hidden Markov chain process. We derive an exact, explicit and closed-form solution for European-style lookback options in a two-state regime switching model.