Modeling Dependence of Operational Loss Frequencies

Abstract

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.