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


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


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


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


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


    (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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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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00973922, HAL.
  3. Alexandru Badescu & Robert J. Elliott & Juan-Pablo Ortega, 2012. "Quadratic hedging schemes for non-Gaussian GARCH models," Papers 1209.5976,, revised Dec 2013.


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