Proxying credit curves via Wasserstein distances

Credit risk plays a key role in financial modeling, and financial institutions are required to incorporate it in their pricing, as well as in capital requirement calculations. A common manner to extract credit worthiness information for existing and potential counterparties is based on the Credit Default Swap (CDS) market. Nonetheless, not all counterparties of a financial institution have (liquid) CDSs traded in the market. In this case, financial institutions shall employ a proxy methodology to estimate the default probabilities of these counterparties. Starting from the intersection methodology for credit curves, in this article we investigate whether it is possible to construct proxy credit curves from CDS quotes by means of (weighted) Wasserstein barycenters. We show how, under simple and common assumptions, this revised methodology leads to elementary and intuitive formulae to calculate distances between CDS-implied default probability distributions. Further, we illustrate how to use this information to construct proxy CDS quotes.