Body and Tail - Separating the distribution function by an efficient tail-detecting procedure in risk management

TL;DR

This paper introduces an efficient tail-detection procedure for risk management that accurately separates tail data from the overall distribution without prior parameter assumptions, improving tail risk modeling.

Contribution

The paper presents a novel method based on weighted mean square error to identify tail data subsets without parameter specifications, enhancing tail risk modeling accuracy.

Findings

Effective separation of tail data demonstrated on standard financial distributions.

Application to MSCI World Index data for risk quantification.

Goodness of fit tests validate the tail model quality.

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 method that can separate the required subset. 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. 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. In addition, for the MSCI World Index, we use historical data to identify the tail model and to compute the quantiles required for a risk assessment.