Pricing VIX Options with Realized Volatility

We investigate the role of realized volatility in pricing VIX options by using the generalized affine realized volatility (GARV) model, and the Realized generalized autoregressive conditionally heteroscedastic (GARCH) model. We develop a closed‐form pricing formula for the (affine) GARV model. For the (nonaffine) log‐linear Realized GARCH model, we introduce a novel approximation approach to derive its analytical pricing formula. Empirical results show that models with realized volatility significantly outperform competing models based on daily returns only, both in‐ and out‐of‐sample. The Realized GARCH model offers the best pricing performance, as it has fewer constraints and a more flexible modeling structure.