Operational risk quantification using extreme value theory and copulas: from theory to practice
In this talk we present 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 the Value-at-Risk as a risk measure may lead to a mis-estimation 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 it is standard in operational risk.