A comparative analysis of the predictive power of implied volatility indices and GARCH forecasted volatility

• Time-dependent variance or conditional heteroskedasticity is a source of inefficiency.
• Time-dependent variance can be controlled by a GARCH volatility specification.
• Comparing GARCH and Implied volatility forecasts is a robust procedure.
• Out-of-sample (OOS) encompassing tests are adequate to predict forecasting accuracy.
• OOS GARCH volatility forecasts outperform OOS Implied volatility forecasts.

This paper examines the accuracy of implied volatility and GARCH forecasted volatility to predict the behavior of realized volatility. The methodology adopted addresses the information content, the bias, the efficiency and the efficiency forecast of the predictor.In previous studies on this topic, efficiency has been analyzed both in terms of the efficiency of the predictor itself and its forecasting efficiency. In this context, implied volatility is the predictor and the efficiency is assessed through the validation of some of the OLS (Ordinary Least Squares) assumptions. However, those studies paid little attention to the heteroskedasticity of the residuals, even though this is an important source of inefficiency. Our study accounts for conditional heteroskedasticity by using a GARCH model to predict the time-dependent variance of the residuals. A GARCH forecasted volatility index was constructed based on these estimates.In addition, we employ out-of-sample forecasting accuracy tests in order to identify the best forecasting model. The results clearly show that GARCH forecasted volatility outperforms implied volatility to produce out-of-sample forecasts based on a subsample of the total sampling period for the four stock markets analyzed.