Copula-Dependent Defaults in Intensity Models

30 Pages Posted: 10 Mar 2002

Date Written: December 2001


In this paper we present a new approach to incorporate dynamic default dependency in intensity-based default risk models. The model uses an arbitrary default dependency structure which is specified by the Copula of the times of default, this is combined with individual intensity-based models for the defaults of the obligors without loss of the calibration of the individual default-intensity models. The dynamics of the survival probabilities and credit spreads of individual obligors are derived and it is shown that in situations with positive dependence, the default of one obligor causes the credit spreads of the other obligors to jump upwards, as it is experienced empirically in situations with credit contagion. For the Clayton copula these jumps are proportional to the pre-default intensity. If information about other obligors is excluded, the model reduces to a standard intensity model for a single obligor, thus greatly facilitating its calibration. To illustrate the results they are also presented for Archimedean copulae in general, and Gumbel and Clayton copulae in particular. Furthermore it is shown how the default correlation can be calibrated to a Gaussian dependency structure of CreditMetrics-type.

Keywords: Credit Risk, Default Correlation, Credit Derivatives

JEL Classification: G13

Suggested Citation

Schönbucher, Philipp J. and Schubert, Dirk, Copula-Dependent Defaults in Intensity Models (December 2001). Available at SSRN: or

Philipp J. Schönbucher (Contact Author)

ETH Zürich - Department of Mathematics ( email )

ETH Zentrum HG-F 42.1
Raemistr. 101
CH-8092 Zurich, 8092
+41 1 6326409 (Phone)


Dirk Schubert

KPMG ( email )