"Solving the Esscher puzzle" - The NEF-GHS option pricing model

With the celebrated model of Black and Scholes in 1973 the development ofmodern option pricing models started. One of the assumptions of the Blackand Scholes model is that the risky asset evolves according to a geometricBrownian motion which implies normally distributed log-returns. As variousempirical investigations show, log-returns do not follow a normal distribution,but are leptokurtic and to some extend skewed. To capture these distributionalstylized facts, exponential Lévy motions have been proposed since1994 which allow for a large class of underlying return distributions. In thesemodels the Esscher transformation is used to obtain a risk-neutral valuationformula. This paper proposes the so-called Esscher NEF-GHS option pricingmodel, where the price process is modeled by an exponential NEF-GHS Lévymotion, implying that the returns follow an NEF-GHS distribution. The correspondingmodel seems to unify all advantages of other Esscher-based optionpricing model, that is numerical tractability and a exible underlying distributionwhich itself is self-conjugate.