Asymptotics for Operational Risk Quantified with Expected Shortfall

In this paper we estimate operational risk by using the convex risk measure Expected Shortfall (ES) and provide an approximation as the confidence level converges to 100% in the univariate case. Then we extend this approach to the multivariate case, where we represent the dependence structure by using a Levy copula as in Bocker and Kluppelberg (2006) and Bocker and Kluppelberg, C. (2008). We compare our results to the ones obtained in Bocker and Kluppelberg (2006) and (2008) for Operational VaR and discuss their practical relevance.

Keywords: Operational risk, Expected Shortfall, Levy copula, regular variation.