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 …

We develop an empirically highly accurate discrete-time daily stochastic volatility model that explicitly distinguishes … inter-dependencies among the shocks to returns and the two different volatility components. The model estimates suggest that … the leverage effect, or asymmetry between returns and volatility, works primarily through the continuous volatility …