Copula-based top-down approaches in financial risk aggregation

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