Continuity correction for barrier options in jump-diffusion models

TL;DR

This paper investigates the continuity correction for barrier options within jump-diffusion models, utilizing the maximum of the underlying process and connections to Bessel processes to improve pricing accuracy.

Contribution

It introduces a novel approach to express barrier option pay-offs through the maximum of jump-diffusion processes and leverages Bessel process connections for better correction methods.

Findings

Provides a new framework for barrier option correction in jump models

Connects maximum of jump-diffusion processes with Bessel processes

Enhances accuracy of barrier option pricing in jump environments

Abstract

The aim of this paper is to study the continuity correction for barrier options in jump-diusion models. For this purpose, we express the pay-off a barrier option in terms of the maximum of the underlying process. We then condition with respect to the jump times and to the values of the underlying at the jump times and rely on the connection between the maximum of the Brownian motion and Bessel processes.