Computing the credit loss distribution in the Gaussian copula model: a comparison of methods

ABSTRACT This paper compares methods for computing the distribution of loss from defaults in a credit portfolio. The methods are applied in the Gaussian copula framework for credit risk and take advantage of the conditional independence of defaults in this framework. As a benchmark we use vanilla Monte Carlo simulation to estimate the tail probabilities of the total losses of the credit portfolio. The first method to be compared is a recursive algorithm to obtain the exact distribution of the total loss of the portfolio, conditional on observed values for the systematic risk factors. Then, we apply the saddlepoint approximation to the distribution of the losses, which has proven to give very accurate approximations in the tail. Finally, the method of numerically inverting the Laplace transform of the tail distribution of the losses of the credit portfolio, conditional on observed systematic risk factors, is combined with Euler summation to obtain an approximation. We compare and rank these methods in terms of mean square errors for a fixed computing time. Perhaps surprisingly, we find that vanilla Monte Carlo is hard to beat.