Limiting Loss distribution on a Hierarchical copula-based model

Formulae for the distribution of a counting variable representing the losses of a loan portfolio, that are both realistic and simple to be implemented are hard to come by. Starting from the limiting Gaussian approach (see Vasicek, 1987, 1997) and from the Marshall-Olkin (1988) algorithm and the limiting loss distributions derived in Sch¨onbucher (2004) we propose a procedure for the computation of the loss probability distribution allowing us to take into account the not-exchangeable behavior of a portfolio clusterized into several large classes of homogeneous loans. The clusterized copula-based limiting approach, following the idea of the clustering statistical method proposed in Bernardi and Romagnoli (2011a, 2011b), recovers a possible risks’ hierarchy.