Exploring Dynamic Default Dependence

Abstract

Characterizing the dependence between companies’ defaults is a central problem in the credit risk literature, and the dependence structure is a first order determinant of the value of credit portfolios and structured credit products such as collateralized debt obligations (CDO), as well as the relative values of CDO tranches. We compare correlation measures implied by CDO prices with time-varying correlations implied by equity returns and CDS spreads. We use flexible dynamic equicorrelation techniques introduced by Engle and Kelly (2008) to capture time variation in CDS-implied and equity return-implied correlations. We perform this analysis using North American firms from the CDX index, as well as European firms from the iTraxx index. All correlation time series are highly time-varying and persistent, and correlations extracted from CDSs and CDOs increased significantly in European and North American markets during the turbulent second half of 2007. Interestingly, we find that the correlation time-series implied by CDO prices co-moves very strongly with the correlation time-series extracted from CDS spreads, but somewhat less strongly with the correlations between equity returns. These findings suggest that the cross-sectional dependence in these complex structured products is fairly well measured. However, changes in CDO prices may be due to changes in correlation, and more sophisticated models with time-varying correlations are thus needed to value CDOs.