ABSTRACT
The assessment of the joint default probability of groups of obligors, as well as related notions, such as the probability that the n-th one of them defaults, is a crucial problem in credit risk. To solve it, both the industry and the academia have extensively relied on copula methods. These allow to split any joint default probability into the marginal ones and a function, the copula itself, which represents only the association or dependence between defaults. Essentially, the splitting up makes both default modeling and calibration much easier, since it permits separate fitting at the univariate and joint level. At present, the use of copula techniques is a well-established fact in risk modeling and credit derivative pricing. However, the choice of the copula and its calibration is still an open issue: model risk indeed exists at both stages, and its understanding relies on a deep discussion of the current practices and model limitations.
