Volatility activity: Specification and estimation

The paper examines volatility activity and its asymmetry and undertakes further specification analysis of volatility models based on it. We develop new nonparametric statistics using high-frequency option-based VIX data to test for asymmetry in volatility jumps. We also develop methods for estimating and evaluating, using price data alone, a general encompassing model for volatility dynamics where volatility activity is unrestricted. The nonparametric application to VIX data, along with model estimation for S&P index returns, suggests that volatility moves are best captured by an infinite variation pure-jump martingale with a symmetric jump compensator around zero. The latter provides a parsimonious generalization of the jump-diffusions commonly used for volatility modeling.