Realized GARCH, CBOE VIX, and the Volatility Risk Premium

TL;DR

This paper demonstrates that the Realized GARCH model provides a closed-form expression for the VIX and VRP, explaining their dynamics and outperforming traditional GARCH models in empirical tests with S&P 500 data.

Contribution

It introduces a Realized GARCH framework that captures the volatility risk premium and VIX dynamics with a closed-form solution, improving upon existing models.

Findings

Realized GARCH yields close-form VIX and VRP expressions.

The model explains time-variation in the VRP.

Outperforms conventional GARCH models in empirical analysis.

Abstract

We show that the Realized GARCH model yields close-form expression for both the Volatility Index (VIX) and the volatility risk premium (VRP). The Realized GARCH model is driven by two shocks, a return shock and a volatility shock, and these are natural state variables in the stochastic discount factor (SDF). The volatility shock endows the exponentially affine SDF with a compensation for volatility risk. This leads to dissimilar dynamic properties under the physical and risk-neutral measures that can explain time-variation in the VRP. In an empirical application with the S&P 500 returns, the VIX, and the VRP, we find that the Realized GARCH model significantly outperforms conventional GARCH models.