Long vs. short term asymmetry in volatility and the term structure of risk

This short paper introduces the distinction between short and long term asymmetric effects in volatilities. With short term asymmetry we refer to the conventional one, i.e. the asymmetric response of current volatility to the most recent return shocks. In addition, we argue that there may be asymmetries with respect to the way the effect of past return shocks propagate over time. We refer to this as long term asymmetry and propose a model that enables the study of the potential occurrence of such a feature. In an empirical application using stock market index data we find evidence of the joint presence of short and long term asymmetric effects and demonstrate important implications for risk predictions. In particular, positive return shocks is ascribed substantial significance for long term risk prediction.