Modeling dependence of operational loss frequencies

Modeling dependence among operational loss frequencies is a natural way of trying to capture possible relationships between losses, which are categorized differently with respect to the business line or the event type, but which have occurred simultaneously. We propose a model that explicitly accounts for such dependence and allows modeling it in a heterogeneous way to capture the wide spectrum of dependence structures operational losses exhibit. Our model relies on a pair copula construction, which flexibly combines different bivariate copulas, to estimate efficiently the joint multivariate distribution and then determine the total risk capital. Empirical results on real-world data show that such flexible explicit dependence modeling might have a significant impact on the risk capital, leading to a clear diversification benefit compared to the standard Basel comonotonicity assumption.