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, we interpret the effect of the riskneutralization, and we derive approximation procedures which allow for a computationally efficient implementation of the model. When the model is estimated on financial returns data the results indicate that compared to the Gaussian case the extension is important. A study of the model properties shows that there are important option pricing differences compared to the Gaussian case as well as to the symmetric special case. A large scale empirical examination shows that our model outperforms the Gaussian case for pricing options on three large US stocks as well as a major index. In particular, improvements are found when considering the smile in implied standard deviations.