On the Consistency of “European Proxy” of Structural Models for Credit Derivatives

In this paper, we focus on what we call “European Proxy” of structural models, or shortly “ProxyStructural 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 “Proxy-Structural models”, by contrast, the path condition modeling the default indicator function is replaced by a pointwise 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.