Good Volatility, Bad Volatility, and VIX Futures Pricing: Evidence from the Decomposition of VIX

Realized semivariance, computed from intraday positive/negative squared returns, provides an accurate measure of the upside/downside variations of stock returns. This article investigates the role of realized semivariance in pricing the CBOE VIX and VIX futures, using a realized semivariance-based model. We obtain the closed-form pricing formula for the VIX index and VIX futures prices, and show that the new model provides superior pricing performance, both in-sample and out-of-sample. We further analytically derive the pricing formulas for the upside/downside components of the VIX (risk-neutral semivariance). Such a decomposition shows that the information gains from the conventional unsigned realized variance are concentrated on pricing the downside part of the VIX; the new realized semivariance-based model provides a larger and more balanced improvement for both the upside and downside components of the VIX. Our results provide strong evidence that the spread between upside/downside variance is the main driver of the asymmetry in return distributions.