Directly pricing VIX futures with observable dynamic jumps based on high‐frequency VIX

Abstract

AbstractThis 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.