Estimating financial risk under time-varying extremal return behavior

Potentially increasing volatility and downside risk is essential to financial risk management which is concerned with the tails, or particularly, the lower tail, of the distribution of speculative asset returns. Applying extreme value theory, the present paper outlines a simple model capturing time-varying tail behavior and studies conditional daily return quantiles for the German DAX. Our results indicate an overall increased risk of large one-day holding-period losses related to a structural break given by the 1987 crash, systematic out-of-sample underestimation of the magnitude of extreme quantiles as well as clustering in estimated quantile exceedances which cannot be fully explained by the forecasting model.