Pricing vulnerable lookback options using Laplace transforms

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 establi...

Full description

Saved in:
Bibliographic Details
Published in:Journal of computational and applied mathematics Vol. 451; p. 116014
Main Authors: Wang, Xinying, Zhou, Ke
Format: Journal Article
Language:English
Published: Elsevier B.V 01.12.2024
Subjects:
First passage time
Jump–diffusion
Laplace transforms
Lookback options
Vulnerable options
G13
First passage time
Lookback options
Laplace transforms
Vulnerable options
Jump–diffusion
ISSN:0377-0427
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0377-0427
DOI:10.1016/j.cam.2024.116014