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The Esscher-EGB2 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 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

Suggested Citation

  • Fischer, Matthias J., 2000. "The Esscher-EGB2 option pricing model," Discussion Papers 31/2000, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
    • Handle: RePEc:zbw:faucse:312000
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    References listed on IDEAS

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    1. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    2. 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.
    3. McDonald, James B., 1991. "Parametric models for partially adaptive estimation with skewed and leptokurtic residuals," Economics Letters, Elsevier, vol. 37(3), pages 273-278, November.
    4. Fischer, Matthias J., 2000. "The folded EGB2 distribution and its application to financial return data," Discussion Papers 32/2000, Friedrich-Alexander University Erlangen-Nuremberg, Chair of Statistics and Econometrics.
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    Cited by:

    1. Hang Lin & Lixin Liu & Zhengjun Zhang, 2023. "Tail Risk Signal Detection through a Novel EGB2 Option Pricing Model," Mathematics, MDPI, vol. 11(14), pages 1-32, July.
    2. Svetlozar Rachev & Frank J. Fabozzi & Boryana Racheva-Iotova & Abootaleb Shirvani, 2017. "Option Pricing with Greed and Fear Factor: The Rational Finance Approach," Papers 1709.08134, arXiv.org, revised Mar 2020.

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