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Dynamic Copula Processes: A new way of modelling CDO tranches

by Daniel Totouom of BNP Paribas, and
Margaret Armstrong of École des Mines de Paris

November 2005

Abstract: We have developed a new family of Archimedean copula processes for modeling the dynamic dependence between default times in a large portfolio of names and for pricing synthetic CDO tranches. After presenting their general properties, we show that there is a class of processes where default is not predictable. Then we study a new Clayton copula process in detail. Using CDS data as at July 2005, we show that the base correlations given by this model at the standard detachment points are very similar to those quoted in the market for a maturity of 5 years.

JEL Classification: G13.

Keywords: default risk, CDOs, correlation smile, Archimedean copulas, multivariate stochastic processes.

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