Asymmetries and Volatility Regimes in the European Equity Markets

This paper provides and empirical examination of four European equity indices between 1991 and 2005. We investigate the ability of fifteen different GARCH models to capture the characteristics of historical daily returns effectively and generate realistic implied volatility skews. Using many different model selection criteria we conclude that a normal mixture GARCH model with two volatility components, two sources of asymmetry and endogenous time-varying conditional higher moments provides the best fit overall. Since this model is relatively new in the literature we discuss the theoretical and empirical properties of such models. Examining the estimated parameters we show that they provide information on the likelihood of a crash and they specify the return and volatility behaviour, the leverage effect and the persistence of volatility during the two regimes ('normal' and 'crash'). We also find that asymmetric normal mixture GARCH models, even without a volatility risk premium, afford a sufficiently rich structure to match the empirical characteristics of implied volatility skew surfaces, whereas single-state GARCH models give unrealistic shapes for the equity index skew.