Volatility in Equilibrium: Asymmetries and Dynamic Dependencies
52 Pages Posted: 14 Apr 2010 Last revised: 6 May 2010
Date Written: March 19, 2010
Stock market volatility clusters in time, appears fractionally integrated, carries a risk premium, and exhibits asymmetric leverage effects relative to returns. At the same time, the volatility risk premium, defined by the difference between the risk-neutral and objective expectations of the volatility, is distinctly less persistent and appears short-memory. This paper develops the first internally consistent equilibrium based explanation for all of these empirical facts. The model is cast in continuous-time and entirely self-contained, involving non-separable recursive preferences. Our empirical investigations are made possible through the use of newly available high-frequency intra-day data for the VIX volatility index, along with corresponding high-frequency data for the S&P 500 aggregate market portfolio. We show that the qualitative implications from the new theoretical model match remarkably well with the distinct shapes and patterns in the sample auto-correlations and dynamic cross-correlations in the returns and volatilities observed in the data.
Keywords: Equilibrium asset pricing, stochastic volatility, leverage effect, volatility feedback, option implied volatility, realized volatility, variance risk premium
JEL Classification: C22, C51, C52, G12, G13, G14
Suggested Citation: Suggested Citation