Analyticity of the Wiener-Hopf factors and valuation of exotic options in L\'evy models

TL;DR

This paper develops analytical formulas for valuing exotic path-dependent options in Lévy models by leveraging Wiener-Hopf factorization and Fourier methods, enabling precise pricing of options like lookbacks and default swaps.

Contribution

It introduces new analytical expressions for the characteristic functions of extrema of Lévy processes, facilitating improved valuation of complex options.

Findings

Derived explicit formulas for supremum and infimum characteristic functions

Provided valuation formulas for one-touch, lookback, and default swap options

Enhanced Fourier-based pricing methods for Lévy models

Abstract

This paper considers the valuation of exotic path-dependent options in L\'evy models, in particular options on the supremum and the infimum of the asset price process. Using the Wiener--Hopf factorization, we derive expressions for the analytically extended characteristic function of the supremum and the infimum of a L\'evy process. Combined with general results on Fourier methods for option pricing, we provide formulas for the valuation of one-touch options, lookback options and equity default swaps in L\'evy models.