Barrier Options under L\'evy Processes: a Simple Short-Cut

TL;DR

This paper introduces a straightforward method for pricing barrier options driven by a wide range of Lévy processes, leveraging market symmetry assumptions for simplicity and providing approximations when symmetry is absent.

Contribution

It offers a novel, simple approach to barrier option pricing under Lévy processes, expanding applicability through symmetry-based approximations.

Findings

Method simplifies barrier option pricing under Lévy processes

Applicable to a broad class of Lévy models with symmetry

Provides approximation techniques when symmetry assumptions are violated

Abstract

In this paper we present a very simple way to price a class of barrier options when the underlying process is driven by a huge class of L\'evy processes. To achieve our goal we assume that our market satisfies a symmetry property. In case of not satisfying that property some approximations can be obtained.