Pricing CDO's Based on the Multivariate Wang Transform

This paper shows that the one-factor Gaussian copula model, the standard market model for valuing CDO’s, can be derived from the multivariate Wang transform, which is consistent with Buhlmann’s equilibrium pricing model, whence it has a sound economic interpretation. The Gaussian copula model is then extended within the Buhlmann’s framework. Unlike the existing models, our model calibrates the parameter associated with risk aversion index of the representative investor, not the correlation parameter. A t-copula model is also considered to describe the fat-tail distribution observed in the actual markets.

Keywords: One-factor Gaussian copula model, Merton’s structural model, Buhlmann’s economic premium principle, multivariate Wang transform, Student t distribution.