  We follow a long path for Credit Derivatives and Collateralized Debt
Obligations (CDOs) in particular, 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. En passant, we also illustrate the implied
copula, a method that can consistently account for CDOs with different
attachment and detachment points but not for different maturities. The
discussion is abundantly supported by market examples through history. The
dangers and critics we present to the use of the Gaussian copula and of implied
correlation had all been published by us, among others, in 2006, showing that
the quantitative community was aware of the model limitations before the
crisis. We also explain why the Gaussian copula model is still used in its base
correlation formulation, although under some possible extensions such as random
recovery. Overall we conclude that the modeling effort in this area of the
derivatives market is unfinished, partly for the lack of an operationally
attractive single-name consistent dynamic loss model, and partly because of the
diminished investment in this research area.
