On Wasserstein distances, barycenters, and the cross-section methodology for proxy credit curves

Abstract

The credit default swap (CDS) market plays an important role for financial institutions. This is not only for their trading activities, but also as it provides a source of information to extract default probabilities to be used for (counterparty) credit risk purposes, as for instance in credit valuation adjustment calculations. Nonetheless, the number of entities for which liquid single-name CDSs are traded is of the order of a few thousands. This requires financial institutions to employ proxy methodologies to estimate the credit risk they face when trading with counterparties for which no (liquid) CDSs are available in the market. In this paper, we propose and compare different approaches to take into account counterparty-specific information in terms of rating, region, sector, etc. at cross-sectional level to strip risk-neutral default probabilities from CDSs. This is achieved by taking into account the intrinsic probabilistic information characterizing each CDS by means of suitably-defined Wasserstein distances and barycenters. The results suggest that default probabilities are likely to be overestimated if the construction of the proxy credit curves overlooks the probability structure underlying the CDS market, potentially resulting in a too conservative counterparty credit risk pricing framework.