The static hedging of CDO tranche correlation risk

Abstract

This article gives examples illustrating the static hedging of Collateratized debt obligation (CDO) correlation risk. Changes in correlation result in changes in the relative portioning out of the total expected loss of a reference portfolio to the different tranches. Thus, portfolios with low correlation risk contain a number of CDO tranches whose weights are adjusted, so that the daily changes in the mark-to-market values of the different tranches tend to cancel out. Example portfolios are backtested for immunization against correlation and index spread risks using iTraxx CDO market spreads for the challenging period following the 5 May 2005 Standard and Poor's downgrade of Ford and General Motors. The implementation is carried out by using the static loss-surface model of Walker [CDO Models – Towards the Next Generation: Incomplete Markets and Term Structure, 2005. Available at http://www.physics.utoronto.ca/~qocmp/nextGenDefaultrisk.pdf; CDO Valuation: Term Structure, Tranche Structure, and Loss Distributions, 2006. Available at http://www.physics.utoronto.ca/~qocmp/nextLongB.2006.09.22.pdf] and Torresetti et al. [Implied Expected Tranched Loss Surface from CDO Data, 2006. Available at http://www.damianobrigo.it].

Keywords:

• CDOs
• hedging
• correlation risk

2000 AMS Subject Classification :

• 91Bxx:91B24

Acknowledgements

I thank Julien Houdain and Fortis Investments for providing the market quotes used in the examples. The support of the Natural Sciences and Engineering Research Council of Canada is acknowledged.