Fast CDO analytics: Some cool results for an uncool model

Bjorn Flesaker (Bloomberg)

Despite its severe theoretical and practical shortcomings, players in the large market for synthetic CDO tranches continue to make heavy use of the single factor Gaussian copula model with base correlation. We present a new decomposition result for the portfolio loss distribution that draws on an analogy to the decomposition of European options into time value and intrinsic value. We derive a closed form solution for the "intrinsic value component" of a tranche, and we show that the "time value component" of a tranche is approximately time independent, once suitably centered. Putting it all together, we obtain an implementation that is capable of generating the model value along with single name spread and default sensitivities very rapidly.