Forecasting the volatility index using Real-Time Realized EGARCH-FHS model

We propose the Real-Time Realized GARCH-FHS model which combines the Real-Time Realized EGARCH (REGARCH) model with the filtered historical simulation (FHS) method to enhance forecasting accuracy for the Chicago Board Options Exchange Volatility Index (VIX). The proposed model simultaneously incorporates intraday extreme-value information and current return information, while offering flexibility in measurement transformations and effectively capturing the non-Gaussian characteristics of innovation distributions. To evaluate its predictive performance, we conduct a comprehensive empirical analysis using four CBOE Volatility Indices: VIX9D, VIX, VIX3M, and VIX6M. Empirical results demonstrate that the Real-Time REGARCH-FHS model consistently outperforms benchmark models in terms of both in-sample and out-of-sample forecasting accuracy for the VIX. Moreover, robustness analysis confirms that the superior predictive performance of the Real-Time REGARCH-FHS model is robust to alternative weights used in the optimization function, alternative weights used in the loss function, alternative realized measures, alternative optimization function, alternative volatility states, pricing results based on three indices and the Model Confidence Set (MCS) test. Further discussion illustrates that the Real-Time REGARCH model can also be applied to forecast Bitcoin returns volatility. In summary, our findings highlight the importance of incorporating intraday extreme-value and current return information in enhancing VIX forecasting accuracy.