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

  • 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)

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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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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