A copula-based hierarchical hybrid loss distribution

Abstract

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 classified as `large' or `small' depending on their cardinality. The hierarchical hybrid copula-based 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 and we 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 high-dimensional problems. We study the scalability of the algorithm.