On GARCH and Autoregressive Stochastic Volatility Approaches for Market Calibration and Option Pricing

In this paper, we carry out a comprehensive comparison of Gaussian generalized autoregressive conditional heteroskedasticity (GARCH) and autoregressive stochastic volatility (ARSV) models for volatility forecasting using the S&P 500 Index. In particular, we investigate their performance using the physical measure (also known as the real-world probability measure) for risk management purposes and risk-neutral measures for derivative pricing purposes. Under the physical measure, after fitting the historical return sequence, we calculate the likelihoods and test the normality for the error terms of these two models. In addition, two robust loss functions, the MSE and QLIKE, are adopted for a comparison of the one-step-ahead volatility forecasts. The empirical results show that the ARSV(1) model outperforms the GARCH(1, 1) model in terms of the in-sample and out-of-sample performance under the physical measure. Under the risk-neutral measure, we explore the in-sample and out-of-sample average option pricing errors of the two models. The results indicate that these two models are considerably close when pricing call options, while the ARSV(1) model is significantly superior to the GARCH(1, 1) model regarding fitting and predicting put option prices. Another finding is that the implied versions of the two models, which parameterize the initial volatility, are not robust for out-of-sample option price predictions.