Implied Correlations in CDO Tranches

by Nicole Lehnert of the Universität Karlsruhe,
Frank Altrock of WestLB AG,
Svetlozar T. Rachev of the Universität Karlsruhe & University of California, Santa Barbara,
Stefan Trück of Queensland University of Technology, and
Andre Wilch of WestLB AG

December 20, 2005

Abstract: Market quotes of CDO tranches constitute a market view on correlation at different points in the portfolio capital structure and thus on the shape of the portfolio loss distribution. We investigate different calibrations of the CreditRisk+ model to examine its ability to reproduce iTraxx tranche quotes. Using initial model calibration, CreditRisk+ clearly underestimates senior tranche losses. While sensitivities to correlation are too low, by increasing PD volatility up to about 3 times of the default probability for each name CreditRisk+ produces tails which are fat enough to meet market tranche losses. Additionally, we find that, similar to the correlation skew in the large pool model, to meet market quotes for each tranche a different PD volatility vector has to be used.

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Related reading: " Valuing Credit Derivatives Using an Implied Copula Approach"