Pricing VIX Options with Realized Volatility

Abstract

It is well known that realized measures of volatility, which are computed from high-frequency intraday data, provide accurate measurements of the latent volatility process. We investigate the role of realized volatility in pricing VIX options using the GARV model (Christoffersen et al., 2014), and the Realized GARCH model (Hansen et al., 2012). A closed-form pricing formula for the (affine) GARV model is developed. For the (non-affine) log-linear Realized GARCH model, we introduce a novel approximation approach to derive its analytical pricing formula. We show that the newly proposed approximation method is fast, with a high degree of accuracy. An extensive empirical application on VIX options from 2006 to 2020 shows that models with realized volatility significantly outperform conventional GARCH-type models based on daily returns only. Among these, the Realized GARCH model provides the best pricing performance due to its fewer constraints and a more flexible modeling structure. Our results hold both in-sample and out-of-sample.

Keywords: Realized GARCH, Realized Volatility, VIX Options, VIX Derivatives

JEL Classification: G12, G13, C51, C52