Robust Estimation of Operational Risk

TL;DR

This paper introduces robust statistical procedures for estimating the tail quantiles of operational risk loss distributions, addressing challenges like outliers and data pooling, with application to real industry data.

Contribution

It develops and applies optimally-robust methods (MBRE, OMSE, RMXE) for GPD parameter estimation in operational risk, improving stability over classical techniques.

Findings

Robust methods provide more stable estimates in the presence of outliers.

Application to industry data demonstrates practical effectiveness.

Diagnostic plots support the robustness and reliability of the estimates.

Abstract

According to the Loss Distribution Approach, the operational risk of a bank is determined as 99.9% quantile of the respective loss distribution, covering unexpected severe events. The 99.9% quantile can be considered a tail event. As supported by the Pickands-Balkema-de Haan Theorem, tail events exceeding some high threshold are usually modeled by a Generalized Pareto Distribution (GPD). Estimation of GPD tail quantiles is not a trivial task, in particular if one takes into account the heavy tails of this distribution, the possibility of singular outliers, and, moreover, the fact that data is usually pooled among several sources. Moreover, if, as is frequently the case, operational losses are pooled anonymously, relevance of the fitting data for the respective bank is not self-evident. In such situations, robust methods may provide stable estimates when classical methods already fail. In this paper, optimally-robust procedures MBRE, OMSE, RMXE are introduced to the application domain of operational risk. We apply these procedures to parameter estimation of a GPD at data from Algorithmics Inc. To better understand these results, we provide supportive diagnostic plots adjusted for this context: influence plots, outlyingness plots, and QQ plots with robust confidence bands.