Pricing American Options when the Underlying Asset follows GARCH processes

As extensions to the Black-Scholes model with constant volatility, option pricing models with time-varying volatility have been suggested within the framework of generalized autoregressive conditional heteroskedasticity (GARCH). However, application of the GARCH option pricing model has been hampered by the lack of simulation techniques able to incorporate early exercise features. In the present paper, we show how new simulation techniques can be used to price options which have the possibility of early exercise in a GARCH framework. We report the results from an extensive Monte Carlo study, indicating that incorporating GARCH features in the option pricing model can potentially help explain some empirically well documented systematic pricing errors. Our empirical analysis of out of sample performance shows that GARCH effects are important when pricing options on individual stocks and lead to improvements over the constant volatility model. Specifications of the exponential GARCH type generally have the smallest pricing errors. JEL Classification: C22, C53, G13