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

48 Pages Posted: 1 Mar 2012 Last revised: 29 Dec 2015

Zhaogang Song

Johns Hopkins University - Carey Business School

Dacheng Xiu

University of Chicago - Booth School of Business

Date Written: April 12, 2015

Abstract

Using both S&P 500 option and recently introduced VIX option prices, we study pricing kernels and their dependence on multiple volatility factors. We first propose nonparametric estimates of marginal pricing kernels, conditional on the VIX and the slope of the variance swap term structure. Our estimates highlight the state-dependence nature of the pricing kernels. In particular, conditioning on volatility factors, the pricing kernel of market returns exhibit a downward sloping shape up to the extreme end of the right tail. Moreover, the volatility pricing kernel features a striking U-shape, implying that investors have high marginal utility in both high and low volatility states. This finding on the volatility pricing kernel presents a new empirical challenge to both existing equilibrium and reduced-form asset pricing models of volatility risk. Finally, using a full-fledged parametric model, we recover the joint pricing kernel, which is not otherwise identifiable.

Keywords: Multi-Factor Volatility Model, Pricing Kernel, Variance Swaps, VIX Options

JEL Classification: G12, G13

Suggested Citation

Song, Zhaogang and Xiu, Dacheng, A Tale of Two Option Markets: Pricing Kernels and Volatility Risk (April 12, 2015). Fama-Miller Working Paper, Forthcoming; Chicago Booth Research Paper No. 12-10. Available at SSRN: https://ssrn.com/abstract=2013381 or http://dx.doi.org/10.2139/ssrn.2013381

Zhaogang Song

Johns Hopkins University - Carey Business School ( email )

100 International Drive
Baltimore, MD 21202
United States

Dacheng Xiu (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

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