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Remarks on Pricing Correlation Products

by Harald Skarke of Bank Austria Creditanstalt

July 17, 2005

Abstract: The standard approach for the risk neutral pricing of correlation products such as CDOs is to apply a one factor Gaussian copula model with certain variations. This model can be expressed as an average over scenarios where, conditional on a parameter, default time distributions for different obligors are independent. Using this description I show that the Gaussian copula approach leads to certain predictions concerning relative changes of default probabilities that are not only counterintuitive but also in disagreement with market data. These problems can be avoided within the framework of conditional independence by changing the forms of the conditional default time probability distributions away from what is dictated by the Gaussian copula assumption. This leads to a class of models that do not require modifications such as using the base correlation technique; this class contains the model recently suggested by Hull and White.

Keywords: Correlation, one factor model, Gaussian copula.

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