Option Pricing under GARCH models with Generalized Hyperbolic innovations (I) : Methodology

Abstract

In this paper, we present an alternative to the Black Scholes model for a discrete time economy using GARCH-type models for the underlying asset returns with Generalized Hyperbolic (GH) innovations that are potentially skewed and leptokurtic. Assuming that the stochastic discount factor is an exponential affine function of the states variables, we show that this class of distributions is stable under the Risk neutral change of probability.GARCH, Generalized Hyperbolic Distribution, pricing, risk neutral distribution.