Dynamic Credit Correlation Modelling
by Claudio Albanese of the Imperial College London,
May 12, 2006
Abstract: As the market for credit baskets and single tranche bespoke CDOs keeps growing very rapidly, we witness a lively debate about the merits and shortcomings of the base correlation model, which is currently the recognized market standard. Difficulties such as the lack of arbitrage-freedom and the witnessed impossibility to calibrate in some market situations are motivations to research a different standard for mark-to-market and risk management. To contribute to this ongoing debate, we describe here a new modeling framework based on a structural, bottom-up approach. Points of interest for this model are that it can be made consistent with many data sources such as rating transition probabilities, historical default probabilities, single name credit spread curves and equilibrium recovery swap rates. Remarkably enough, we find that the model can be calibrated simultaneously to synchronous datasets for the iTraxx and CDX term structures for tranche spreads across the entire capital structures, including the index basis, and for maturities up to 10 years. The model makes use of an innovative mathematical framework based on spectral analysis and provides numerically noiseless spreads and hedge ratios. As far as execution times are concerned, the model is at least as fast if not faster than the most simplified analytic versions of the base correlation model.
Keywords: dynamic credit correlation modelling, single tranche bespoke CDOs, credit basket basis, term structure of tranche spreads.