Pricing VIX Futures and Options With Good and Bad Volatility of Volatility

ABSTRACT This article studies the pricing of VIX futures and options by directly modeling the dynamics of VIX, based on realized semivariances computed from high‐frequency data of VIX. We derive the closed‐form pricing formula for both the VIX futures and options. The empirical results show that the new model provides superior pricing performance compared with the model based on conventional unsigned realized variance and the classic Heston‐Nandi GARCH model, both in sample and out of sample. Our study confirms that the decomposition of realized variance into upside and downside components helps to improve the pricing performance for VIX futures and options.