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Title:Solving the Esscher puzzle: the NEF-GHS option pricing model PDF Logo
Authors:Fischer, Matthias J.
Issue Date:2002
Series/Report no.:Diskussionspapiere // Friedrich-Alexander-Universität Erlangen-Nürnberg, Lehrstuhl für Statistik und Ökonometrie 42a/2002
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 is that the risky asset evolves according to a geometric Brownian motion which implies normally distributed log-returns. As various empirical investigations show, log-returns do not follow a normal distribution, but are leptokurtic and to some extend skewed. To capture these distributional stylized facts, exponential Lévy motions have been proposed since 1994 which allow for a large class of underlying return distributions. In these models the Esscher transformation is used to obtain a risk-neutral valuation formula. This paper proposes the so-called Esscher NEF-GHS option pricing model, where the price process is modeled by an exponential NEF-GHS Levy motion, implying that the returns follow an NEF-GHS distribution. The corresponding model seems to unify all advantages of other Esscher-based option pricing model, that is numerical tractability and a flexible underlying distribution which itself is self-conjugate.
Subjects:NEF-GHS distribution
Option pricing
Esscher transformation
JEL:C22
G13
Document Type:Working Paper
Appears in Collections:Diskussionspapiere des Lehrstuhls für Statistik und Ökonometrie, FAU Erlangen-Nürnberg

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