On break-even correlation: the way to price structured credit derivatives by replication

Abstract

We consider the pricing of European-style structured credit pay-off under the Gaussian Copula Model (GCM). When no sudden jump-to-default events occur, the perfect replication of these pay-offs under the GCM is obtained if and only if the underlying single-name credit spreads follow a particular family of dynamics and if the pricing parameters are given by so-called 'break-even' correlations. We exhibit a class of Merton-style models that are consistent with this result. We calculate breakeven correlations explicitly to price nth-to-default baskets under the GCM. Finally, we illustrate the usefulness of this concept as a relative-value tool.

Dynamic Hedging of Synthetic CDO Tranches: Bridging the Gap between Theory and Practice

“…If one were to observe the path of assets associated with different names instead associated with the multivariate structural model are well understood and lead to perfect replication of CDO tranches when concentrating on spread risk (defaults are predictable), we can think of deltas coming out of the Gaussian copula model to have some economic significance 23 . As discussed above, Fermanian and Vigneron (2009) propose a different approach. They look for some dynamic models consistent with the credit spread deltas obtained from the Gaussian copula model.…”

“…Names cluster together according to the level of credit spreads and credit deltas are either equal to zero or one (see Burtschell et al (2009) for a detailed analysis). For instance, when looking at an equity tranche, the names with the highest credit spreads have a delta equal to one 38 , while the remaining names have a delta equal to zero. Such a phenomenon also occurs in the stochastic correlation model described by Burtschell et al (2007).…”

“…The higher the increase of credit spread deltas with respect to the level of spreads, the higher will the corresponding idiosyncratic gamma 39 . 38 There is always a matter of norm. Here the reference is the credit default swap index.…”