A copula-based hierarchical hybrid loss distribution

We propose a model for the computation of the loss probability distribution allowing to take into account the not-exchangeable behavior of a portfolio clustered into several classes of homogeneous loans. These classes are classied as ‘large’ or ‘small’ depending on their cardinality. The hierarchical hybrid copulabased model (HHC for short) follows the idea of the clusterized homogeneous copula-based approach (CHC) and its limiting version or the limiting clusterized copula-based model (LCC) proposed in our earlier work. This model allows us to recover a possible risk hierarchy. We suggest an algorithm to compute the HHC loss distribution andwe compare this cdf with that computed through the CHC and LCC approaches (in the Gaussian and Archimedean limit) and also with the pure limiting approaches which are commonly used for highdimensional problems. We study the scalability of the algorithm.