Levy Density Based Intensity Modeling of the Correlation Smile

The jump distribution for the default intensities in a reduced form framework is modeled and calibrated to provide reasonable fits to CDX.NA.IG and iTraxx Europe CDOs, to 5, 7 and 10 year maturities simultaneously. Calibration is carried out using an efficient Monte Carlo simulation algorithm suitable for both homogeneous and heterogeneous collections of credit names. The underlying jump process is found to relate closely to a maximally skewed stable Levy process with index of stability alpha ~ 1.5.