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Solving the Esscher puzzle: the NEF-GHS option pricing model

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  • Fischer, Matthias J.

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.

Suggested Citation

  • Fischer, Matthias J., 2002. "Solving the Esscher puzzle: the NEF-GHS option pricing model," Discussion Papers 42a/2002, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
  • Handle: RePEc:zbw:faucse:42a2002
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    File URL: https://www.econstor.eu/bitstream/10419/29624/1/614039215.pdf
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    References listed on IDEAS

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    Cited by:

    1. Fischer, Matthias J., 2002. "Skew generalized secant hyperbolic distributions: unconditional and conditional fit to asset returns," Discussion Papers 46/2002, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    2. Fabozzi, Frank J. & Leccadito, Arturo & Tunaru, Radu S., 2014. "Extracting market information from equity options with exponential Lévy processes," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 125-141.

    More about this item

    Keywords

    NEF-GHS distribution; Option pricing; Esscher transformation;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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