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Extending Gaussian Copula with Jumps to Match Correlation Smile

by Geng Xu of Wachovia Securities

December 18, 2006

Abstract: We present an extension to the Gaussian copula model with jumps. We mix normal distributions which have negative means and small weights with the standard normal distribution in the Gaussian copula model to generate jumps in the default probability distribution for each underlying credit. The means and weights of the new normal distributions are used to control the size and intensity of the jumps. Our model can replicate the type of default probability distribution observed in Hull-White's implied copula model. It has a perfect fit with the recent iTraxx index tranche market prices, and uses different approach than the existing stochastic correlation model.

JEL Classification: G13.

Keywords: synthetic CDO, loss distribution, recursive method, compound Poisson approximation, normal power approximation.

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