Joint threshold exceedances of stock index returns in bull and bear periods

The investigation of extreme returns on financial assets is motivated, among others, by financial risk assessment. We investigate joint distributions of threshold excesses of daily returns on several stock indices, threshold meaning the 10%, respectively 90%, quantile of the return distribution. In a first step, the generalized Pareto distribution is fitted to a return series, then the logistic dependence function is used to couple pairs of threshold excess distributions. One of our goals is to compare the behaviour of exceedances in bull and bear periods and relate it to the degree of dependency found in their joint distributions.