Mathematical Finance Seminar
November 15, 2001 , 5:30 PM to 7:00 PM
Phillip Schoenbucher, University of Bonn
Copula-Dependent Default Risk in Intensity Models
In this paper we present a new approach to incorporate 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.