Factor Copula Model For Portfolio Credit Risk

A critical aspect in the valuation and risk management of multi-name credit derivatives is the modeling of the dependence among sources of credit risk. The dependence modeling poses difficulties in the pricing of a multi-name credit derivatives, in the estimation of the value-at-risk of a portfolio, or in the pricing of some other basket credit derivative as the description not only on the default arrival in an individual reference entity but on the default dependence among entities in the portfolio should be considered. Although the elliptical models have been widely used due to their mathematical tractability, the dependence modeling using the multi-dimensional Lévy process has shown growing interest among researchers despite its complexity. In this paper, we introduce one factor copula model for portfolio credit risk based on Normal Tempered Stable (NTS) distribution and calibrate the model through 5-year synthetic Collateralized Debt Obligation (CDO) tranche spreads under a large homogeneous portfolio approximation. The calibration results show that the one factor copula model based on NTS distribution is more flexible and provides a dependence structure fitting market CDO tranche spreads. As one of the major applications of the dependence modeling in credit risk, this model shares the advantage of the Gaussian one factor model, and all extensions and implementation methods used for it can be utilized.