On CDO Tranche Pricing when Copula is Nearly Comonotone

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On CDO Tranche Pricing when Copula is Nearly Comonotone

by Andrey Chirikhin of HSBC

August 8, 2008

Abstract: Pricing of a CDO base tranche is considered when copula is comonotone and approximations are derived for the base tranche expected loss, obtained with a one-factor Gaussian copula model, when correlations are sufficiently close to 100%. Numerical examples are provided showing that a two-term approximation reproduces the true value with no more than approximately 5% relative error, uniformly across detachments and average default probabilities for correlations between 95% and 100%.

Keywords: credit, CDO, credit crunch, Gaussian copula, comonotone copula, quadrature, approximation.

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