Fitting the CDO correlation skew: a tractable structural jump-diffusion model

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 February 2007 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 0.1% within five years. 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.