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CDO 2 Pricing Using Gaussian Mixture Model with Transformation of Loss Distribution

by David X. Li of Barclays Capital, and
Michael Hong Liang of Barclays Capital

September 5, 2005

Abstract: We present a new approach to price CDOˆ2-type transactions consistently with the pricing of the underlying CDOs. We first present an extension to the current market standard model using a Gaussian mixture (GM) copula model instead of one parameter single Gaussian Copula model. It shows that GM broadly captures the correlation skew shown in the index tranche market, but not exactly and across time or across term structure. Then using an analogy to the option pricing for CDO tranche pricing we extract an implied loss distribution from the observed index tranche market or a set of bespoke pricing of the underlying baby portfolios. To strike a balance of matching the underlying baby CDO pricing and having a plausible economic correlation model to price CDOˆ2-type trades we create a loss distribution transformation for each baby CDO portfolio between the implied loss distribution from the index tranche market or bespoke pricing and the loss distribution from the GM model. This way, we can match the pricing for all baby portfolios or tranches, and at the same time, we price bespoke CDO and CDOˆ2 with a broadly skew aware correlation model. In the future we could further calibrate the parameters in the GM model to the CDOˆ2 market if its pricing becomes more observable.

Keywords: CDO Squared, Implied loss distribution, loss distribution transformation, Gaussian mixture copula.

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