A Factor-Copula Based Valuation of Synthetic CDO-Squared under Stochastic Intensity

Abstract

This study extends the double student’s t factor copula models developed by Hull and White (2004) for valuing CDO-Squared. First, the assumptions of non-homogeneous recovery rates are adopted to fit realistic aggregate loss of CDO collateral. Second, a stochastic hazard rate is proposed using the CIR intensity process to resolve the problem of inability of constant intensity rate to capture instantaneous credit spread dynamics. To construct the default probability distribution of CDO-Squared, the factor copula model is derived using the two-stage probability bucketing method to approximate loss distribution. Finally, the example of CDO-Squared issued by the Polaris Securities Group in Taiwan is presented to illustrate fair credit spread pricing for various tranches.