Body and tail: an automated tail-detecting procedure

Ingo Hoffmann and Christoph Börner

Abstract

In risk management, tail risks are of crucial importance. The quality of a tail model, which is determined by data from an unknown distribution, depends critically on the subset of data used to model the tail. Based on a suitably weighted mean square error, we present a completely automated method that can separate the required subset of data to model the tail. The selected data are used to determine the parameters of the tail model. Notably, no parameter specifications have to be made to apply the proposed procedure in the automatic evaluation of large amounts of data. Standard goodness-of-fit tests allow us to evaluate the quality of the fitted tail model. We apply the method to standard distributions that are usually considered in the finance and insurance industries. We consider the MSCI World Index as our example. We analyze historical data to identify the tail model and calculate the high quantiles required for a risk assessment.