A large literature has been devoted to the evaluation of CDO tranches in a cross-section setting. The main idea is that the cross-section dependence of the times to default of the assets or names of the securitization deal is specified, the dynamics of the losses in the pool of credits is simulated accordingly and the value of tranches is recovered. The dependence structure is usually represented in terms of copula functions, which provides flexibility and allows to separate the specification of marginal default probability distributions and dependence. The application of copula was first proposed by Li (2000) and nowadays is a common practice in the market of basket credit derivatives, particularly in the version of factor copulas (see Gregory and Laurent (2005) for a review and Burtshell, Gregory and Laurent (2005) for a comparison of the approach). This approach is obviously feasible for CDOs with a limited number of assets. Even for those, however, there is an issue that remains to be solved, and it has to do with the temporal consistency of prices.
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Cherubini, U., Mulinacci, S., Romagnoli, S. (2009). A Copula-Based Model of the Term Structure of CDO Tranches. In: Härdle, W.K., Hautsch, N., Overbeck, L. (eds) Applied Quantitative Finance. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69179-2_3
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