Operational Risk Aggregation across Business Lines Based on Frequency Dependence and Loss Dependence

In loss distribution approach (LDA), the most popular approach in operational risk modeling, frequency dependence and loss distribution dependence across business lines are two dependences which banks should consider. In practice, mainly for simplicity, many banks only model frequency dependence although they think that the impact of frequency dependence is insignificant. In this study, two approaches, respectively, models frequency dependence and loss distribution dependence, are introduced. Both approaches are modeled by copula function, which is capable of capturing nonlinear correlation. Based on the most comprehensive operational risk dataset of Chinese banking as far as we know, the operational risk capital charge of the overall Chinese banking is calculated by the two approaches. The results show that there is an obvious distinction between the capital calculated by modeling frequency dependence and the capital calculated by modeling loss dependence. The approach with very limited attention exactly yields a much larger capital result. So it is advised in this paper that banks should not just rely on the approach to modeling frequency dependence for it is natural and easy to deal with. A safer and more effective way for banks is to comprehensively take the results of the two kinds of approach into consideration.