Bocker and Kluppelberg [Risk Mag., 2005, December, 90-93] presented a simple approximation of OpVaR of a single operational risk cell. The present paper derives approximations of similar quality and simplicity for the multivariate problem. Our approach is based on the modelling of the dependence structure of different cells via the new concept of a Levy copula.Dependence model, Levy copula, Multivariate dependence, Multivariate Levy process, Operational risk, Pareto distribution, Regular variation, Subexponential distribution,

Simultaneous modelling of operational risks occurring in different event type/business line cells poses a serious challenge for operational risk quantification. Here we invoke the new concept of Lévy copulas to model the dependence structure of operational loss events. We explain the consequences of this dependence concept for frequencies and severities of operational risk in detail. For important examples of the Lévy copula and heavy-tailed GPD tail severities we derive first order approximations for multivariate operational VAR.

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We investigate the problem of modelling and measuring multidimensional operational risk.Based on the very popular univariate loss distribution approach, we suggest an "invariance principle" which should be satisfied by any multidimensional operational risk model, and which is naturally fulfilled by our modelling technique based on the new concept of Pareto Lévy copulas. Our approach allows for a fully dynamic modelling of operational risk at any future point in time. We exploit the fact that operational loss data are typically heavy-tailed, and, therefore, we intensively discuss the concept of multivariate regular variation, which is considered as a very useful tool for various multivariate heavy-tailed phenomena. Moreover, for important examples of the Pareto Lévy copulas and appropriate severity distributions we derive first order approximations for multivariate operational Value-at-Risk.