On the aggregation of credit, market and operational risks

Risk aggregation considering inter-risk dependence has always been a challenge to both researchers and practitioners. The objective of this study is to formulate ways of aggregation of bank risks and comprehensively compare simple summation, variance–covariance and copula approach. Firstly, the three popular approaches are adopted to aggregate credit risk, market risk and operational risk of banks based on Austrian banking data. Then, two comparisons are mainly made. Total risks aggregated by different approaches are compared to analyze their relative magnitudes. Diversification benefits of different approaches are further compared to investigate their tail dependence structures. Based on the empirical analysis, some facts are verified and some interesting findings are uncovered, leading to the conclusions that simple summation approach is too conservative and variance–covariance approach is overly optimistic, so it is suggested that copula approach is the future major trend for bank risk aggregation. Especially, t copula with degree of freedom between 1 and 10 is a good choice to capture tail dependence while Gaussian copula is not recommended. Besides, the proposed mixture copula consisting of t copula and Gumbel copula exhibits heavier right tail dependence than single t copula.