An empirical comparison of copula models to value collateralized debt obligation

Abstract

In this paper, we consider a one-factor copula approach to value collateralized debt obligations (CDOs). We implement Hull and White (2004)’s idea of dispersion in pair-wise correlation to Double-t model, and compare the Double-t model with four other model specifications including one-factor Gaussian copula, Gaussian copula with dispersion in correlation, Double-t model with dispersion in correlation and T copula. We find although the dispersion in correlation can improve the goodness of fit for one-factor Gaussian copula, it does not contribute to the model fit for Double-t model. We further examine the effect of tail dependence on the performance of the five copula models and calibrate those models to market data of CDX and iTraxx tranches, and find Double-t model with constant correlation provides the best fit