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Dynamic Copulas and Forward Starting Credit Derivatives

by Daniel Totouom of BNP Paribas
Margaret Armstrong of Ecole des Mines de Paris

February 20, 2007

Abstract: In this paper dynamic copula processes are used to price forward starting credit derivatives instruments. Building on previous work (Totouom and Armstrong 2007a and b) we show that the new type of compound gamma process developed is in fact a Levy process. Then we extend the dynamic copula processes initially designed for a bullet exposure to the case of a forward starting credit derivative instruments while retaining the lower tail dependence. The new model automatically reproduces the CDS and forward CDS spreads, so it is a market model. One advantage of this copula-based approach is that it separates the underlying spread calibrations from that of the dependence structure (correlation). The asymptotic behaviour of both the spot copula and the forward copula is given, in much the same way as Vasicek did with the Gaussian copula.

JEL Classification: G13.

Keywords: default risk, CDOs, Forward Starting CDOs, correlation smile, Archimedean copulas, multivariate stochastic processes, lower tail dependence.

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