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A comparison of pricing kernels for GARCH option pricing with generalized hyperbolic distributions. (English) Zbl 1282.91116

Summary: 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.

MSC:

91B25 Asset pricing models (MSC2010)
91G20 Derivative securities (option pricing, hedging, etc.)
91G70 Statistical methods; risk measures
60G42 Martingales with discrete parameter
62P05 Applications of statistics to actuarial sciences and financial mathematics
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