Synthetic CDO Squared Pricing Methodologies

Dominique Guegan () and Julien Houdain
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Dominique Guegan: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Julien Houdain: IDHE - Institutions et Dynamiques Historiques de l'Economie - ENS Cachan - École normale supérieure - Cachan - UP1 - Université Paris 1 Panthéon-Sorbonne - UP8 - Université Paris 8 Vincennes-Saint-Denis - UPN - Université Paris Nanterre - CNRS - Centre National de la Recherche Scientifique

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Abstract: We propose two different methodologies for the pricing of CDO squared and by extension for the risk management of funds of CDO tranches. The first methodology is based on a drill-down approach whereas the second one is based on a "correlation of correlation" approach. Our purpose is to be consistent with the inner CDOs characteristics because of several issues that need to be addressed. The correlation "skew" of each underlying inner CDO must be reproduced. The outer correlation, the correlation of joint loss distributions, among the losses of the inner CDOs must be considered. The outer correlation, which can be interpreted as a global correlation "skew", depends on the overlapping characteristics, the spread level and recovery rate assumptions for each credit in the portfolio, and the correlation structure among the credits. We demonstrate that using these approaches we can obtain a very good proxy for complex structures prices in the correlation market. Nevertheless we have to mention some theoretical drawbacks. The drill-down methodology is consistent with the outer correlation but assumes that prices of the inner tranches are driven by the same market correlation "skew". The "correlation of correlation" approach is consistent with inner tranches pricing but not with the outer correlation. We also illustrate the fact that the pricing should be very sensitive to the level of outer correlation when we use the "correlation of correlation" methodology. We demonstrate that using these two methodologies we can now efficiently price CDO squared and risk manage funds of CDO tranches.

Keywords: correlation of correlation; Fund of CDOs; CDO of CDOs; CDO squared; Correlation "skew; "correlation of correlation; Drill-Down; Factor models; NIG; Mapping (search for similar items in EconPapers)
Date: 2008-07
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Published in Greg N. Gregoriou, Paul U. Ali. Credit Derivatives Handbook - Global Perspectives, Innovations, and Market Drivers, MCGraw Hill, 361-377 (chapiter 16), 2008

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00265708

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