Forecasting the Volatility Index with a realized measure, volatility components and dynamic jumps

Xinyu Wu, Yuyao Wang and Bo Zhang

Abstract

This paper proposes a two-component realized exponential generalized autoregressive conditional heteroscedasticity model with dynamic jumps (the REGARCH- 2C-Jump model) to forecast the Chicago Board Options Exchange Volatility Index (VIX). This model is able to capture high-frequency information, long-memory volatility and time-varying jump intensity simultaneously. We obtain the risk-neutral dynamic of the REGARCH-2C-Jump model and derive the corresponding model-implied VIX formula. Our in-sample results indicate that the proposed model has superior empirical fitting compared with competing models. Out-of-sample empirical results suggest that our REGARCH-2C-Jump model outperforms competing models in forecasting the VIX. Moreover, its superior forecasting performance is robust to different sample periods and an alternative realized measure. Further analysis demonstrates that the nonaffine REGARCH-2C-Jump model outperforms Wang andWang’s generalized affine realized volatility model with hidden components and jumps (the GARV-2C-Jump model) in out-of-sample VIX forecasting. Our empirical findings provide strong support for incorporating a realized measure, a component volatility structure and dynamic jumps in the context of a nonaffine framework in order to improve VIX forecasts.