Modeling dependence of operational loss frequencies

Eike Christian Brechmann, Claudia Czado and Sandra Paterlini

Abstract

ABSTRACT

Modeling dependence among operational loss frequencies is a natural way of trying to capture possible relationships between losses that have occurred simultaneously but that are categorized differently with respect to the business line or the event type. We propose a model that explicitly accounts for such dependence and allows it to be modeled in a heterogeneous way in order to capture the wide spectrum of dependence structures that 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 determines the total risk capital. Empirical results on real-world data show that such flexible explicit dependence modeling might have a significant impact on risk capital, leading to a clear diversification benefit compared with the standard Basel comonotonicity assumption.