American Option Pricing using GARCH models and the Normal Inverse Gaussian distribution

Abstract

In this paper we propose a feasible way to price American options in a model with time varying volatility and conditional skewness and leptokurtosis using GARCH processes and the Normal Inverse Gaussian distribution. We show how the risk neutral dynamics can be obtained in this model using the Generalized Local Risk Neutral Valuation Relationship of Duan (1999) and we derive approximation procedures which allows for a feasible implementation of the model. A Monte Carlo study shows that there are important pricing differences compared to the Gaussian case. When the model is estimated the results indicate that compared to the Gaussian case the extensions are important. A large scale empirical examination confirms this finding and shows that our model outperforms the Gaussian case for pricing options on three large US stocks. In particular, improvements are found for out of the money options and short term options. These are among the most traded and the suggested model is therefore important.