Robust Estimators in Generalized Pareto Models

TL;DR

This paper develops robust estimation methods for generalized Pareto distributions, crucial for modeling extreme events like operational risk, ensuring reliable inference despite data deviations.

Contribution

It introduces optimally-robust estimators tailored for GPDs, enhancing the reliability of extreme value analysis in financial risk management.

Findings

Robust estimators effectively bound influence of outliers.

Application to Basel II operational risk modeling.

Improved accuracy in tail quantile estimation.

Abstract

This paper deals with optimally-robust parameter estimation in generalized Pareto distributions (GPDs). These arise naturally in many situations where one is interested in the behavior of extreme events as motivated by the Pickands-Balkema-de Haan extreme value theorem (PBHT). The application we have in mind is calculation of the regulatory capital required by Basel II for a bank to cover operational risk. In this context the tail behavior of the underlying distribution is crucial. This is where extreme value theory enters, suggesting to estimate these high quantiles parameterically using, e.g. GPDs. Robust statistics in this context offers procedures bounding the influence of single observations, so provides reliable inference in the presence of moderate deviations from the distributional model assumptions, respectively from the mechanisms underlying the PBHT.