Fast solution of the Gaussian copula model

This article describes a new approach to compute values and sensitivities of synthetic collateralized debt obligation (CDO) tranches in the market-standard, single-factor, Gaussian copula model with base correlation. We introduce a novel decomposition of the conditional expected capped portfolio loss process into “intrinsic value” and “time value” components, derive a closed form solution for the intrinsic value, and describe a very efficient computational scheme for the time value, taking advantage of a curious time stability of this quantity.