An Introduction to Lévy Processes and Their Application to Option Pricing

Abstract

This paper intends to provide a friendly introduction to Lévy processes and mainly focuses on valuing contingent claims when the price of the underlying asset is driven by such processes. Moreover, several analytical results on the characteristic function of an infinitely divisible distribution are discussed, which are very useful in pricing financial options living out of the Gaussian world. In contrast with the Black-Scholes pricing methodology that uses density functions, this approach uses characteristic functions. Finally, explicit formulas for valuing options on assets following Lévy regular processes are provided.