Realised Co-Skewness of the VIX and S&P 500 and the Equity Premium

Abstract

We provide theoretical and empirical justifications for linking the realised co-skewness between the VIX and the S&P 500 to conditional equity premiums. The realised co-skewness, as a measure of hedging benefits, shows a significant (and independent to that of the variance risk premium) negative prediction for the next month equity premium. We also present a new measure of higher co-moments using high frequency data under the general jump diffusion model. The estimator is robust to the presence of market microstructure noise and can be extended to other co-moment measurement in current risk management practices.

Keywords: Itˆo Variance hedging; Co-skewness; Stock return prediction; High frequency data; Market microstructure noise; Pre-averaging

JEL Classification: C13, C14, G10, G12