A Comparison of GARCH Option Pricing Models Using Bayesian Inference and Implied Calibration

This paper presents a comparison between the pricing performance of option implied GARCH models and the Bayesian GARCH option pricing model and a generalization thereof that employs a regime switching feature. An algorithm is presented that shows how option prices can be computed using a Markov switching GARCH model from a Bayesian perspective and detailed information is presented about the inference techniques. The estimated models are tested empirically by forecasting out-of-sample S&P500 index option prices over the year 2014 and the results are compared with 2 competitive benchmark models. The results show that the option implied GARCH and the Markov switching GARCH models substantially outperform the simple GARCH model. The Markov switching GARCH can compete quite well with the option implied models and generally outperforms these models for medium and long maturities.