Operational Risk Quantification Using Extreme Value Theory and Copulas: From Theory to Practice
Journal of Operational Risk, 3 (2009), 1--24.
30 Pages Posted: 15 Jul 2008 Last revised: 27 Nov 2013
Date Written: July 15, 2008
Abstract
In this paper we point 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 diversification may be inappropriate when infinite-mean distributions are involved.
Keywords: Extreme Value Theory, Copula Theory, Value-at-Risk, Sub-additivity, Coherence
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