Modeling Volatility of S&P 500 Index Daily Returns: A comparison between model based forecasts and implied volatility

The objective of this study is to investigate the predictability of model based forecasts and the VIX index on forecasting future volatility of S&P 500 index daily returns. The study period is from January 1990 to December 2010, including 5291 observations. A variety of time series models were estimated, including random walk model, GARCH (1,1), GJR(1,1) and EGARCH (1,1) models. The study results indicate that GJR (1,1) outperforms other time series models for out-of-sample forecasting. The forecast performance of VIX, GJR(1,1) and RiskMetrics were compared using various approaches. The empirical evidence does not support the view that implied volatility subsumes all information content, and the study results provide strong evidence indicating that GJR (1,1) outperforms VIX and RiskMetrics for modeling future volatility of S&P 500 index daily returns. Additionally, the results of the encompassing regression for future realized volatility at 5-, 10-, 15-, 30and 60-day horizons, and the results of the encompassing regression for squared return shocks suggest that the joint use of GJR (1,1) and RiskMetrics can produce the best forecasts. By and large, our finding indicates that implied volatility is inferior for future volatility forecasting, and the model based forecasts have more explanatory power for future volatility.