Measuring and Modeling Default Dependence: Evidence from CDO, CDS and Equity Data

Abstract

Characterizing the dependence between companies' defaults is a central problem in the credit risk literature. This dependence structure is a first order determinant of the relative values of structured credit products such as collateralized debt obligations (CDO). We present a number of stylized facts useful in guiding the modeling of default dependence. We systematically compare correlation measures implied from three different markets: base correlations implied by CDO prices, correlations implied by equity returns, and correlations estimated from default intensities implied by CDS prices. We use flexible dynamic equicorrelation techniques introduced by Engle and Kelly (2007) to capture time variation in CDS-implied and equity return-implied correlations while base correlations are obtained using the Gaussian copula. We perform this analysis using American data, the components of the CDX index, as well as European data, the components of the iTraxx index. For each index, there is substantial co-movement between the three correlation time-series. All correlations are highly time-varying and persistent. European and North American correlation series display considerable co-movement. Correlations across both markets increased significantly during the turbulent second half of 2007.