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A Comparison Of Pricing Kernels For Garch Option Pricing With Generalized Hyperbolic Distributions

Author

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  • ALEXANDRU BADESCU

    (Department of Mathematics and Statistics, University of Calgary, Calgary, Canada)

  • ROBERT J. ELLIOTT

    (Department of Mathematical Sciences, University of Adelaide, Adelaide, Australia;
    Haskayne School of Business, University of Calgary, Calgary, Alberta, Canada)

  • REG KULPERGER

    (Department of Statistics and Actuarial Science, University of Western Ontario, London, Ontario, Canada)

  • JARKKO MIETTINEN

    (Department of Mathematics and Statistics, University of Helsinki, Helsinki, Finland)

  • TAK KUEN SIU

    (Department of Applied Finance and Actuarial Studies, Faculty of Business and Economics, Macquarie University, Sydney, Australia)

Abstract

Under discrete-time GARCH models markets are incomplete so there is more than one price kernel for valuing contingent claims. This motivates the quest for selecting an appropriate price kernel. Different methods have been proposed for the choice of a price kernel. Some of them can be justified by economic equilibrium arguments. This paper studies risk-neutral dynamics of various classes of Generalized Hyperbolic GARCH models arising from different price kernels. We discuss the properties of these dynamics and show that for some special cases, some pricing kernels considered here lead to similar risk neutral GARCH dynamics. Real data examples for pricing European options on the S&P 500 index emphasize the importance of the choice of a price kernel.

Suggested Citation

  • Alexandru Badescu & Robert J. Elliott & Reg Kulperger & Jarkko Miettinen & Tak Kuen Siu, 2011. "A Comparison Of Pricing Kernels For Garch Option Pricing With Generalized Hyperbolic Distributions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(05), pages 669-708.
    • Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:05:n:s0219024911006401
    DOI: 10.1142/S0219024911006401
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    References listed on IDEAS

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    1. Christophe Chorro & Dominique Gu�gan & Florian Ielpo, 2012. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1079-1094, April.
    2. Christophe Chorro & Dominique Guegan & Florian Ielpo, 2010. "Option pricing for GARCH-type models with generalized hyperbolic innovations," Post-Print halshs-00469529, HAL.
    3. Barr Rosenberg., 1972. "The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security Prices," Research Program in Finance Working Papers 11, University of California at Berkeley.
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    Cited by:

    1. Chorro, Christophe & Guégan, Dominique & Ielpo, Florian & Lalaharison, Hanjarivo, 2018. "Testing for leverage effects in the returns of US equities," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 290-306.
    2. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    3. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2014. "Quadratic hedging schemes for non-Gaussian GARCH models," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 13-32.
    4. Matthias R. Fengler & Alexander Melnikov, 2018. "GARCH option pricing models with Meixner innovations," Review of Derivatives Research, Springer, vol. 21(3), pages 277-305, October.
    5. Badescu, Alexandru & Elliott, Robert J. & Ortega, Juan-Pablo, 2015. "Non-Gaussian GARCH option pricing models and their diffusion limits," European Journal of Operational Research, Elsevier, vol. 247(3), pages 820-830.

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