Modeling Term Structure of Default Correlation

Abstract

Students of option theory have spent decades trying to find the most plausible way to explain the implied volatility smile. Multi-name credit derivatives feature a similar problem in the form of the correlation skew. Prices for tranche securities with different exposures to the credit risk in an underlying pool of assets are greatly affected by the expected default correlation. But implying that correlation from the market prices of the tranches yields a different value from each one, in a pattern that generally increases with seniority. As with the volatility smile, much modeling effort has gone into trying to smooth out the correlation skew, with only limited success. In this article, the author proposes a new idea—that the correlation skew may be mainly a term structure effect. Because the earliest defaults in a pool will affect the equity tranche first, while the senior tranches can only be hit later, after many defaults have already happened, there is a clear connection between maturity and a tranche’s default risk exposure. This article develops a model of the correlation term structure and shows that it can explain tranche prices surprisingly well, without requiring a very different correlation for each tranche.