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Heterogeneous Credit Portfolios and the Dynamics of the Aggregate Losses

by Paolo Dai Pra of the UniversitÓ di Padova, and
Marco Tolotti of the UniversitÓ Bocconi

December 23, 2008

Abstract: We study the impact of contagion in a network of firms facing credit risk. We describe an intensity based model where the homogeneity assumption is broken by introducing a random environment that makes it possible to take into account the idiosyncratic characteristics of the firms. We shall see that our model goes behind the identification of groups of firms that can be considered basically exchangeable. Despite this heterogeneity assumption our model has the advantage of being totally tractable. The aim is to quantify the losses that a bank may suffer in a large credit portfolio. Relying on a large deviation principle on the trajectory space of the process, we state a suitable law of large number and a central limit theorem useful to study large portfolio losses. Simulation results are provided as well as applications to portfolio loss distribution analysis.

AMS Classification: 60K35, 91B70.

Keywords: Central limit theorems in Banach spaces, Credit contagion, intensity based models, Large Deviations, large portfolio losses, random environment.

Published in: Stochastic Processes and their Applications, Vol. 119, No. 9, (September 2009), pp. 2913-2944.

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