This paper proposes to study volatility index (VIX) futures pricing by directly modeling the logarithmic VIX while incorporating observable dynamic jumps of the VIX, which are derived based on VIX high-frequency data. The impacts of several different interday and intraday jump tests for VIX futures prices are investigated. We obtain the analytical expression by deducing the forward iteration relations of the lagged logarithm VIX, as well as the conditional variance and jump intensity, and use the maximum likelihood method to estimate the parameters under the risk-neutral measure. The empirical results prove the superiority of our newly proposed model (especially the model based on the LM jump test), which indicates that considering the heteroscedasticity effect of conditional variance, introducing VIX high-frequency data information and separating realized jump variation from the realized variance are very important to obtain much more accurate VIX futures pricing.
We propose a novel hybrid approach for volatility index (VIX) futures pricing by combining support vector regression (SVR) with parametric models. Realized semivariances calculated based on high‐frequency VIX are used to characterize the asymmetric shocks of VIX, and the direct pricing framework of the heterogeneous autoregressive model is extended by incorporating realized semivariances. VIX futures prices are first obtained via parametric models, then the predicted prices and realized semivariances are input into SVR to obtain the final predicted values. Empirical results indicate that the combination of SVR with parametric models significantly improves the pricing ability. This indicates the important information of high‐frequency VIX and the necessity of combining machine learning methods with parametric models to obtain more accurate predictions.
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