A General Approach for Lookback Option Pricing under Markov Models

TL;DR

This paper introduces an efficient numerical method for pricing lookback options across diverse Markov models by combining integral representations with Markov chain approximations.

Contribution

It presents a model-agnostic approach that efficiently computes lookback option prices using numerical quadrature and Markov chain techniques.

Findings

Method is applicable to various Markov models including regime-switching and stochastic local volatility.

Numerical examples demonstrate high efficiency and accuracy.

Approach simplifies complex first passage probability calculations.

Abstract

We propose a very efficient method for pricing various types of lookback options under Markov models. We utilize the model-free representations of lookback option prices as integrals of first passage probabilities. We combine efficient numerical quadrature with continuous-time Markov chain approximation for the first passage problem to price lookbacks. Our method is applicable to a variety of models, including one-dimensional time-homogeneous and time-inhomogeneous Markov processes, regime-switching models and stochastic local volatility models. We demonstrate the efficiency of our method through various numerical examples.