degree of volatility risk in stock and index returns, where we characterize volatility risk by the extent to which … forecasting errors in realized volatility are substantive. Even though returns standardized by ex post quadratic variation … distribution of returns. Explicitly modeling this volatility risk is fundamental. We propose a dually asymmetric realized …

mean and volatility. The endogenous structural breakpoint unit root test, ARDL model, and alternative volatility models … price while the volatility of global fertilizer prices and crude oil price from March to December 2008 are higher than in …

memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the …