Huang, Xinzheng, Cornelis W. Oosterlee, "Adaptive Integration for Multi-factor Portfolio Credit Loss Models", Journal of Computational and Applied Mathematics, Vol. 231, No. 2, (September 2009), pp. 506-516.
Abstract: We propose algorithms of adaptive integration for calculation of the tail probability in multi-factor credit portfolio loss models. We first modify the classical Genz-Malik rule, a deterministic multiple integration rule suitable for portfolio credit models with number of factors less than 8. Later on we arrive at the adaptive Monte Carlo integration, which essentially replaces the deterministic integration rule by antithetic random numbers. The latter can not only handle higher-dimensional models but is also able to provide reliable probabilistic error bounds. Both algorithms are asymptotic convergent and consistently outperform the plain Monte Carlo method.
Keywords: Adaptive integration, Genz-Malik rule, Monte Carlo, Credit portfolio loss.