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

This paper proposes a two-component realized exponential generalized autoregres-sive 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-memoryvolatility and time-varying jump intensity simultaneously. We obtain the risk-neutraldynamic of the REGARCH-2C-Jump model and derive the corresponding model-implied VIX formula. Our in-sample results indicate that the proposed model hassuperior empirical fitting compared with competing models. Out-of-sample empir-ical results suggest that our REGARCH-2C-Jump model outperforms competingmodels in forecasting the VIX. Moreover, its superior forecasting performance isrobust to different sample periods and an alternative realized measure. Further analy-sis demonstrates that the nonaffine REGARCH-2C-Jump model outperforms Wangand Wang's generalized affine realized volatility model with hidden components andjumps (the GARV-2C-Jump model) in out-of-sample VIX forecasting. Our empiricalfindings provide strong support for incorporating a realized measure, a component volatility structure and dynamic jumps in the context of a nonaffine framework inorder to improve VIX forecasts.