Portfolio Credit Risk Valuation: An Empirical Analysis Using a Mixture-Weibull Implied Hazard Rate Density

Abstract

Through empirical analysis I show that portfolio credit risk can be valued in a reduced-form framework using hazard rates that are mixture-Weibull distributed. Each mixing density has its own degree of default correlation and probability of observing high default rates. The relative contributions of each density is determined by the mixing weights. How to imply the parameters of the mixture-Weibull distribution by calibrating a CDO valuation model to market spreads is shown. Using two and three mixing densities, I fit the model to daily 5-year CDO spreads for data spanning 2004 to 2008, and I consider CDOs written on both the North American and European investment grade reference portfolios. For the North American CDOs, I report root-mean-squared-errors of 2.009 and 0.713 basis points for the two and three mixture-Weibull models, respectively, while for the European CDOs I report root-mean-squared-errors of 0.953 and 0.220 basis points, respectively. In considering the model during periods of financial distress there is evidence that the dispersion of the implied hazard rate density is increasing in systematic default risk.