Measuring Tail Operational Risk in Univariate and Multivariate Models under Extreme Losses

This paper considers some univariate and multivariate operational risk models, in which the loss severities are modelled by some weakly tail dependent and heavy-tailed positive random variables, and the loss frequency processes are some general counting processes. In such models, we derive some limit behaviors for the Value-at-Risk and Conditional Tail Expectation of aggregate operational risks. The methodology is based on capital approximation within the framework of the Basel II/III regulatory capital accords, which is the so-called Loss Distribution Approach. We also conduct some simulation studies to check the accuracy of our obtained approximations and the (in)sensitivity due to different dependence structures or the heavy-tailedness of the severities.