A Tale of Two Option Markets: Pricing Kernels and Volatility Risk

Abstract:     
The S&P 500 and VIX option markets are closely connected as both options depend on the volatility dynamics. Capturing information in both option prices by nonparametric state-price densities (SPDs), we look into the dynamics of the index and its volatility, along with interactions between the two option markets. We find that SPDs of the index strongly depend on the current VIX level, and that such dependence is driven by information implied from VIX options beyond VIX time series, such as volatility of volatility and volatility skewness. In addition, SPDs of the VIX document three features of its risk-neutral dynamics, including positive skewness, mean-reversion, and high persistence. Moreover, the pricing kernel estimates exhibit a U-shape when the current VIX level is high and a decreasing pattern otherwise, both pre- and post-crisis. This pattern implies that stochastic volatility may be the missing key state variable for the preference of agents, which is responsible for the puzzling U-shape. Finally, we conduct nonparametric specification tests and find that the state-of-the-art stochastic volatility models in the literature cannot capture the S&P 500 and VIX option prices simultaneously. The identified asymmetric mean-reversion rate of volatility suggests non-affine specification as a necessary extension.

Number of Pages in PDF File: 39

Keywords: pricing kernel, state-price density, VIX option, volatility risk

JEL Classification: G12, G13

working papers series