# Finance and Economics Discussion Series

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

Zhaogang Song and Dacheng Xiu
2014-58

Abstract: Using prices of both S&P 500 options and recently introduced VIX options, we study asset pricing implications of volatility risk. While pointing out the joint pricing kernel is not identified nonparametrically, we propose model-free estimates of marginal pricing kernels of the market return and volatility conditional on the VIX. We find that the pricing kernel of market return exhibits a decreasing pattern given either a high or low VIX level, whereas the unconditional estimates present a U-shape. Hence, stochastic volatility is the key state variable responsible for the U-shape puzzle documented in the literature. Finally, our estimates of the volatility pricing kernel feature a U-shape, implying that investors have high marginal utility in both high and low volatility states.

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

Full paper (481 KB PDF)