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On the Consistency of "European Proxy" of Structural Models for Credit Derivatives

by Frédéric D. Vrins of ING Bank

January 2010

Abstract: In this paper, we focus on what we call "European Proxy" of structural models, or shortly "Proxyuctural models" for credit derivatives. In standard structural models, default arrives as the first hit of a stochastic process to a barrier, hence involving a path-dependent condition. In "Proxyuctural models", by contrast, the path condition modeling the default indicator function is replaced by a point-wise criterion. This approximation has been considered by some authors to be successful in the sense that proper calibration of those on CDO market is fast, simple and yields meaningful results in terms of implied prices and parameter movements. Some people may not find them intuitive but up to now, there was no reason to question their relevance for credit derivatives as a whole.

In this paper, we show that this class of models exhibit a philosophical problem, which might potentially have an impact when pricing some specific multivariate credit products other than CDO tranches.

Keywords: Credit Derivatives, Collateralized Debt Obligation, n th to default, Merton models, Dynamic models, Gamma processes.

Published in: Wilmott Journal, Vol. 2, No. 5, (October 2010), pp. 247-260.

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