First-Order Approximations to Operational Risk: Dependence and Consequences
Klaus Böcker and Claudia Klüppelberg
We investigate the problem of modeling and measuring multidimensional operational risk. Based on the very popular univariate loss distribution approach, we suggest an “invariance principle” that should be satisfied by any multidimensional operational risk model and which is naturally fulfilled by our modeling technique based on the new concept of Pareto Lévy copulas. Our approach allows for a fully dynamic modeling 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.
The opinions expressed in this chapter are those of the authors and do not necessarily reflect the views of UniCredit Group. Moreover, measurement concepts presented are not necessarily used by UniCredit Group or any affiliates.


Three years ago, in Böcker and Klüppelberg (2005), we argued that operational risk could be a long-term killer. At that time, perhaps the most spectacular example for a bank failure caused by operational risk losses ...

Get Operational Risk toward Basel III: Best Practices and Issues in Modeling, Management, and Regulation now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.