standard stochastic volatility models and, (ii) the term structure of the at-the-money volatility skew is approximated by a …:(i) has been explained by using fractional volatility model with Hurst index H>1/2, (ii) is proved to be satisfied by a {\it … rough} volatility model with H<1/2 under a risk-neutral measure. This paper provides a solution to this fractional puzzle in …

This paper studies the intertemporal relation between U.S. volatility risk and international equity risk premia. We … show that a common volatility risk factor constructed from the option-implied U.S. forward variances positively and … robust to the inclusion of existing domestic and U.S. predictors and alternative U.S. volatility risk proxies. The …