FACULTÉ & RECHERCHE

The importance of extreme events in finance is increasingly recognized but the existing methods for estimating the tail risk are not very satisfactory. The Hill estimator which is the most commonly used in the literature, suffers severe deficiencies. As an alternative, we propose to estimate the relative tail risk and not the absolute tail risk. This allows us to revisit a larger pool of tail index estimators, including stable law estimators, which have been discarded because of their bias when estimating the absolute tail risk. From a database of 74 international stock market indices, and using both simulated and empirical data, we find that the McCulloch estimator gives an estimate of the relative tail risk up to 50% more precise than the Hill estimator. These results are confirmed by the White (2000) and Hansen (2005) superior predictive ability tests.