Up and Down Volatilities and Their Dynamics

This paper investigates whether positive and negative returns share the same dynamic volatility process. The well established stylized facts on volatility persistence and asymmetric effects are re-examined in light of such dichotomy. To analyze the dynamics of up and down volatilities estimated from daily returns we use a bivariate generalization of the standard EGARCH model. We also investigate various specifications of up and down realized measures estimated from highfrequency data. Our empirical findings point to the existence of a marked diversity in the volatilities of positive and negative returns in terms of sensitivity to past innovations, response to good and bad news and persistence