Volatility forecasting: Downside risk, jumps and leverage effect

We provide empirical evidence of volatility forecasting in relation to asymmetries present in the dynamics of both return and volatility processes. Using recently-developed methodologies to detect jumps from high frequency price data, we estimate the size of positive and negative jumps and propose a methodology to estimate the size of jumps in the quadratic variation. The leverage effect is separated into continuous and discontinuous effects, and past volatility is separated into "good" and "bad", as well as into continuous and discontinuous risks. Using a long history of the S & P500 price index, we find that the continuous leverage effect lasts about one week, while the discontinuous leverage effect disappears after one day. "Good" and "bad" continuous risks both characterize the volatility persistence, while "bad" jump risk is much more informative than "good" jump risk in forecasting future volatility. The volatility forecasting model proposed is able to capture many empirical stylized facts while still remaining parsimonious in terms of the number of parameters to be estimated.