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

TL;DR

This paper investigates the pricing of structured credit derivatives using a static model framework, introducing the concept of break-even correlation to achieve perfect replication under certain conditions.

Contribution

It defines the break-even correlation matrix for structured credit payoff pricing and characterizes when perfect replication is possible within the Gaussian copula model.

Findings

Break-even correlation ensures martingale property of asset prices.

Perfect replication occurs if credit spreads follow specific dynamics.

The paper identifies a class of models consistent with the break-even correlation concept.

Abstract

We consider the pricing of European-style structured credit payoff in a static framework, where the underlying default times are independent given a common factor. A practical application would consist of the pricing of nth-to-default baskets under the Gaussian copula model (GCM). We provide necessary and sufficient conditions so that the corresponding asset prices are martingales and introduce the concept of "break-even" correlation matrix. When no sudden jump-to-default events occur, we show that the perfect replication of these payoffs under the GCM is obtained if and only if the underlying single name credit spreads follow a particular family of dynamics. We calculate the corresponding break-even correlations and we exhibit a class of Merton-style models that are consistent with this result. We explain why the GCM does not have a lot of competitors among the class of one-period static models, except perhaps the Clayton copula.