  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 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 provide also an asymptotically full
capital allocation method. Estimation methods for such tail risk measures and
capital allocations are also proposed and tested on simulated data. Finally, by
having access to real-world operational risk losses from the Italian banking
system, we show that even with a small number of observations, the proposed
estimation methods produce reliable estimates, and 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.
