Adaptive integration for multi-factor portfolio credit loss models

We propose algorithms of adaptive integration for calculation of the tail probability in multi-factor credit portfolio loss models. We first devise 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 simply replaces the deterministic integration rule by pseudo-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.