First order approximations to operational risk - dependence and consequences

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.     «

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 th...     »