VIX forecasting based on GARCH-type model with observable dynamic jumps: A new perspective

This paper proposes to study VIX forecasting based on discrete time GARCH-type model with observable dynamic jump intensity by incorporating high frequency information (DJI-GARCH model). The analytical expression is obtained by deducing the forward iteration relations of vector composed of conditional variance and jump intensity, and parameters are estimated via maximum likelihood functions. To compare the pricing ability, we also present VIX forecasting under four simple GARCH-type models. Results find that DJI-GARCH model outperforms other GARCH-type models for the whole sample and stable period in terms of both in-sample and out-of-sample forecasting, and for the in-sample forecasting during crisis period. This indicates that incorporating both realized bipower and jump variations, and combining VIX information in the estimation can obtain more accuracy forecasting. However, the out-of-sample forecasting using parameters estimated from crisis period shows that GARCH and GJR-GARCH models performs relatively better, which reminds us to be cautious when making out-of-sample prediction.