The Esscher-EGB2 option pricing model

Abstract

With the celebrated model of Black and Scholes in 1973 the development of modern option pricing models started. One of the assumptions of the Black and Scholes model ist that the risky asset evolves according to the geometric brownian motion which implies normal distributed returns. As empirical investigations show, the stock returns do not follow a normal distributions, but are leptokurtic and to some extend skewed. The following paper proposes so-called Esscher-EGB2 option pricing model, where the price process is modeled by an exponential EGB2-Levy-motion, implying that the returns follow an EGB2 distribution and the equivalent martingale measure is given by the Esscher transformation