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Fitting the CDO Correlation Skew: A tractable structural jump-diffusion model

by Søren Willemann of the Aarhus School of Business

November 9, 2005

Abstract: We extend a well-known structural jump-diffusion model for credit risk to handle both correlations through diffusion of asset values and common jumps in asset value. Through a simplifying assumption on the default timing and efficient numerical techniques, we develop a semi-analytic framework allowing for instantaneous calibration to heterogeneous CDS curves and fast computation of CDO tranche spreads. We calibrate the model to CDX and iTraxx data from August 2005 and achieve a satisfactory fit. To price the senior tranches for both indices, we require a risk-neutral probability of a market crash of roughly 0.6%. In the European market, the implied effect from a crash is that all companies come very close to defaulting while the implied effect in the US market is an average loss of 78% in asset value.

JEL Classification: G13, G33.

Keywords: credit risk, structural models, jump-diffusion, CDO, correlation skew.

Published in: Journal of Credit Risk, Vol. 3, No. 1, (Spring 2007), pp. 63-90.

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