Metamodel Of A Large Credit Risk Portfolio In The Gaussian Copula Model

We design a metamodel for the loss distribution L of a large credit risk portfolio in the Gaussian copula model. Our procedure is twofold. We first apply the Wiener chaos decomposition on the normal systemic economic factor and derive a truncated loss L-I at some order I. Then, we provide a Gaussian approximation L-I(G) of the associated truncated loss. Such an approach is motivated by the fact that we are dealing with large portfolios. Our procedure significantly reduces the computational time needed for sampling the loss and therefore for estimating risk measures. The accuracy and effectiveness of our method are confirmed by numerical examples.