Inferring Volatility Dynamics and Risk Premia from the S&P 500 and VIX Markets

Abstract

This paper shows that the VIX market contains information on the variance of the S&P 500 returns, which is not already spanned by the S&P 500 market. We estimate a flexible affine model based on a joint time series of underlying indexes and option prices on both markets. We find that including VIX option prices in the model estimation allows better identification of the parameters driving the risk-neutral conditional distributions and term structure of volatility, thereby enhancing the estimation of the variance risk premium. We gain new insights on the properties of the premium's term structure and show how they can be used to form trading signals. Finally, we show that our premium, used together with a measure of its term structure, has better predictive power on S&P 500 returns compared to the usual model-free premium.

Keywords: S&P 500 and VIX joint modeling, option pricing, particle

JEL Classification: G12, G13, C58.