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Knowledge of the risk-neutral distribution of the cumulative return with respect to the model used, is needed in European option pricing. Duan, Gauthier, Simonato and Sasseville (DGSS) provided an analytic approximation model for the case where an EGARCH or a GJR-GARCH specification is used to describe the asset price dynamics. The DGSS model requires the risk-neutral pricing methodology of the Black-Scholes-Merton (BSM) option pricing model. The Global Financial Crisis (GFC) exposed the shortcomings of the risk-neutral option pricing methodology. In this paper, the DGSS option pricing models are extended to incorporate the Piterbarg option pricing methodology.

The GJR-GARCH and EGARCH option pricing models which incorporate the Piterbarg methodology