Volatility in Equilibrium: Asymmetries and Dynamic Dependencies

Stock market volatility clusters in time, carries a risk premium, is fractionally integrated, and exhibits asymmetric leverage effects relative to returns. This paper develops a first internally consistent equilibrium based explanation for these longstanding empirical facts. The model is cast in continuous-time and entirely self-contained, involving non-separable recursive preferences. We show that the qualitative theoretical implications from the new model match remarkably well with the distinct shapes and patterns in the sample autocorrelations of the volatility and the volatility risk premium, and the dynamic cross-correlations of the volatility measures with the returns calculated from actual high-frequency intra-day data on the S&P 500 aggregate market and VIX volatility indexes.