Copula-based top-down approaches in financial risk aggregation

This article presents the concept of a copula-based top-down approach in the field of financial risk aggregation. Selected copulas and their properties are presented. Copula parameter estimation and goodness-of-fit tests are explained and algorithms for the simulation of copulas and meta-distributions are provided. Further, the dependence structure between interest rate and credit risk factor changes that are computed from sovereign and corporate bond indices is examined. No clear pattern of the dependence structure can be observed as it varies substantially with the duration and the rating of the obligors. This could indicate that top-down approaches are too simplistic to be implemented in practice. However, the results also suggest that copula-based approaches for the data sample at hand seem preferable to the assumption of a multivariate Gaussian distribution as none of the marginal distributions examined are normally distributed and as the Gaussian copula’s fit in terms of the AIC is worse than that of other copulas. Further, the Gaussian copula seems to underestimate the probability of joint strong risk factor changes for the data sample at hand.