Operational risk quantification using extreme value theory and copulas: from theory to practice

Elise Gourier, Walter Farkas, Donato Abbate

Abstract

ABSTRACT

In this paper we perform an empirical study pointing out several pitfalls of the standard methodologies for quantifying operational losses. Firstly, we use extreme value theory to model real heavy-tailed data. We show that using value-at-risk as a risk measure may lead to a misestimation of the capital requirements. In particular, we examine the issues of stability and coherence and relate them to the degree of heavy-tailedness of the data. Secondly, we introduce dependence between the business lines using copula theory. We show that standard economic thinking about risk diversification may be inappropriate when infinite-mean distributions are involved, as is standard in operational risk.