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

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Author Info

  • 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.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Journal of Theoretical and Applied Finance.

Volume (Year): 14 (2011)
Issue (Month): 05 ()
Pages: 669-708

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Handle: RePEc:wsi:ijtafx:v:14:y:2011:i:05:p:669-708

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Related research

Keywords: Option pricing; risk neutral valuation; Generalized Hyperbolic GARCH; extended Girsanov principle; Esscher transform; mean correcting martingale measure; Radon-Nikodym derivative;

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Cited by:
  1. 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.
  2. Christophe Chorro & Dominique Guegan & Florian Ielpo & Hanjarivo Lalaharison, 2014. "Testing for Leverage Effect in Financial Returns," Documents de travail du Centre d'Economie de la Sorbonne 14022, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Science & Finance (CFM) working paper archive 1209.5976, Science & Finance, Capital Fund Management, revised Dec 2013.

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