Comparison Results for Exchangeable Credit Risk Portfolios

by Areski Cousin of the University of Lyon, and
Jean-Paul Laurent of the University of Lyon & BNP Paribas

March 5, 2008

Abstract: This paper is dedicated to the risk analysis of credit portfolios. Assuming that default indicators form an exchangeable sequence of Bernoulli random variables and as a consequence of de Finetti’s theorem, default indicators are Binomial mixtures. We can characterize the supermodular order between two exchangeable Bernoulli random vectors in terms of the convex ordering of their corresponding mixture distributions. Thus we can proceed to some comparisons between stop-loss premiums, CDO tranche premiums and convex risk measures on aggregate losses. This methodology provides a unified analysis of dependence for a number of CDO pricing models based on factor copulas, multivariate Poisson and structural approaches.

JEL Classification: C31, G13.

Keywords: default risk, CDOs, factor copulas, multivariate Poisson, structural models, stochastic orders.

Published in: Insurance: Mathematics and Economics, Vol. 42, No.3, (June 2008), pp. 1118-1127.

Previously titled: Comparison Results for Credit Risk Portfolios

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