Credit models and the crisis: default cluster dynamics and the generalized Poisson loss model

Damiano Brigo, Andrea Pallavicini, Roberto Torresetti

Abstract

ABSTRACT

We consider collateralized debt obligations (CDOs), analyzing their valuation (both pre-crisis and in-crisis) with the generalized Poisson loss model. GeneralizedPoisson loss is an arbitrage-free dynamic loss model capable of calibrating all tranches for all maturities simultaneously. Alternative tranche analysis using the implied copula framework or using historical estimation techniques highlights a multimodal tail in the loss distribution underlying the CDO. An effective description of loss dynamics in terms of the generalized Poisson loss model explains how the multimodal loss-probability distribution can be considered to arise from explicitly modeling the default of subsets of names within the CDO's pool of names. Such default clusters may in turn be interpreted as sectors of the economy. Our discussion is supported by abundant market examples through history, both pre-crisis and in-crisis.