The skewed t distribution for portfolio credit risk
Wenbo Hu, Alec N. Kercheval
Portfolio credit derivatives, such as basket credit default swaps (basket CDS), require for their pricing an estimation of the dependence structure of defaults, which is known to exhibit tail dependence as reflected in observed default contagion. A popular model with this property is the (Student's) t copula; unfortunately there is no fast method to calibrate the degree of freedom parameter.In this paper, within the framework of Schoenbucher's copula-based trigger-variable model for basket CDS pricing, we propose instead to calibrate the full multivariate t distribution. We describe a version of the EM algorithm that provides very fast calibration speeds compared to the current copula-based alternatives. The algorithm generalizes easily to the more flexible skewed t distributions. To our knowledge, we are the first to use the skewed t distribution in this context.