Beyond the Gaussian copula: stochastic and local correlation

Abstract

We consider skew that account for the correlation smile in the pricing of synthetic CDO tranches. These can be viewed as stochastic or local correlation models and are extensions of the well-known one factor Gaussian copula model. We analyse these models through their conditional default probability distributions and marginal compound correlations. We also give some examples of using a particular stochastic correlation model to fit the market, illustrating the stability of the parameters over time. JEL Classification: C 31, G 13