Option Pricing Under the GARCH Framework

In this work, we investigated ways to price options under a heteroskedastic framework in the form of GARCH models. We examined three different GARCH specifications (the standard GARCH, exponential GARCH, and nonlinear asymmetric GARCH) with two different (normal and generalised hyperbolic) conditional distributions. In order to obtain a risk-neutral measure for our GARCH models, we used the Esscher transform and the mean-correcting martingale measure. While the risk-neutral measures derived from these methods agree for the normal case, they differ in the generalised hyperbolic GARCH models. We also investigated two variance reduction techniques in control variates and empirical martingale simulation in order to improve the efficiency of our Monte Carlo simulations that are needed to price the options under the GARCH framework. The results demonstrate the improvement in option pricing performance when we use GARCH specifications with non-Gaussian conditional distributions that can better model the behaviour of the underlying asset.