Pricing vulnerable lookback options using Laplace transforms

Abstract

This study develops a closed-form solution for pricing vulnerable lookback options, which combines the Black–Scholes model for the underlying asset and a correlated jump-diffusion model for the issuer’s asset to account for default risks. Our approach relies on applying Laplace transforms to establish a closed-form solution and compute them numerically using Laplace inversion algorithms. To determine the price, we derive the joint distribution of the first passage time of a drifted Brownian motion and the value of the correlated jump diffusion. Through numerical examples, we demonstrate the accuracy of the numerical solutions obtained through our method and the stability of the algorithm. Subsequently, we conduct a numerical analysis to understand how counterparty risk influences option prices based on our formula.