Credit models and the crisis: An overview

Abstract

This paper describes the evolution of methodologies used to price credit derivatives and collateralised debt obligations (CDOs): from the introduction of the Gaussian copula model and the related implied correlations, to the introduction of arbitrage-free dynamic loss models capable of calibrating all the tranches for all the maturities at the same time; and to the generalised Poisson loss (GPL) model in particular. The paper also discusses: (i) the implied copula model, which can consistently account for CDOs with different attachment and detachment points for a single maturity, and (ii) the notion of expected tranche loss, a model independent quantity that can be easily stripped from CDO data and may be useful for interpolation. The paper also notes that authors had raised objections to using Gaussian copulas and implied correlation in CDO modelling as far back as 2006, showing that the quantitative community was aware of these limitations before the crisis. The authors also comment here on why the Gaussian copulas are still used to model CDOs. Overall, they conclude that more work needs to be done to improve the modelling of CDOs and credit derivatives.