A COMPARISON OF PRICING KERNELS FOR GARCH OPTION PRICING WITH GENERALIZED HYPERBOLIC DISTRIBUTIONS

Alexandru Badescu (), Robert J. Elliott (), Reg Kulperger (), Jarkko Miettinen () and Tak Kuen Siu
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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;
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

International Journal of Theoretical and Applied Finance (IJTAF), 2011, vol. 14, issue 05, 669-708

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.

Keywords: Option pricing; risk neutral valuation; Generalized Hyperbolic GARCH; extended Girsanov principle; Esscher transform; mean correcting martingale measure; Radon-Nikodym derivative (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (6)

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DOI: 10.1142/S0219024911006401

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