Default models based on scale mixtures of Marshall-Olkin copulas: Properties and applications

We present a unification of the Archimedean and the Lévy-frailty copula model for portfolio default models. The new default model exhibits a copula known as scale mixture of Marshall-Olkin copulas and an investigation of the dependence structure reveals that desirable properties of both original models are combined. This allows for a wider range of dependence patterns, while the analytical tractability is retained. Furthermore, simultaneous defaults and default clustering are incorporated. In addition, a hierarchical extension is presented which allows for a heterogeneous dependence structure. Finally, the model is applied to the pricing of CDO contracts. For this purpose, an efficient Laplace transform inversion approach is developed. Supporting a separation of marginal default probabilities and dependence structure, the model can be calibrated to CDS contracts in a first step. In a second step, the calibration of several parametric families to CDO contracts demonstrates a good fitting quality, which further emphasizes the suitability of the approach.