CDO Pricing with Copulae

Modeling the portfolio credit risk is one of the crucial issues of the last years in the financial problems. We propose the valuation model of Collateralized Debt Obligations based on a one- and two-parameter copula and default intensities estimated from market data. The presented method is used to reproduce the spreads of the iTraxx Europe tranches. The two-parameter model incorporates the fact that the risky assets of the CDO pool are chosen from six different industry sectors. The dependency among the assets from the same group is described with the higher value of the copula parameter, otherwise the lower value of the parameter is ascribed. Our approach outperforms the standard market pricing procedure based on the Gaussian distribution.