This paper proposes a generalization of the class of realized semivariance and semicovariance measures introduced by Barndorff-Nielsen, Kinnebrock and Shephard (2010) and Bollerslev, Li, Patton and Quaedvlieg (2020a) to allow for a finer decomposition of realized (co)variances. The new "realized...

The dynamic dependencies in financial market volatility are generally well described by a long-memory fractionally integrated process. At the same time, the volatility risk premium, defined as the difference between the ex-post realized volatility and the market’s ex-ante expectation thereof,...