Modelling Extremal Dependence for Operational Risk by a Bipartite Graph

We introduce a statistical model for operational losses based on heavy-tailed distributions and bipartite graphs, which captures the event type and business line structure of operational risk data. The model explicitly takes into account the Pareto tails of losses and the heterogeneous dependence structures between them. We then derive estimators and provide estimation methods for individual as well as aggregated tail risk, measured in terms of Value-at-Risk and Conditional-Tail-Expectation for very high confidence levels, and introduce also an asymptotically full capital allocation method for portfolio risk. Having access to real-world operational risk losses from the Italian banking system, we apply our model to these data, and carry out risk estimation in terms of the previously derived quantities. Simulation studies further reveal first that even with a small number of observations, the proposed estimation methods produce estimates that converge to the true asymptotic values, and second, that quantifying dependence by means of the empirical network has a big impact on estimates at both individual and aggregate level, as well as for capital allocations. © 2020 Elsevier B.V. All rights reserved