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...

We propose a new decomposition of the realized covariance matrix into components based on the signs of the underlying high-frequency returns. Under an asymptotic setting in which the sampling interval goes to zero, we derive the asymptotic properties of the resulting realized semicovariance...

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...