Fast Computation of Loss Distributions for Credit Portfolios

We pose here an optimization problem related to determining the best set of parameters for minimizing the variance of a Monte Carlo estimator of the probability of a rare event associated with potentially large losses on a portfolio of credit-risky investments. The parameters are associated with a specific importance sampling framework that seeks to sample scenarios with large losses by increasing the default correlation among the portfolio’s assets. Disclaimer: The mathematical framework and questions posed here represent a research project intended to study improvements in computational speed for a general class of Monte Carlo simulations. No inferences should be made with regard to Standard & Poor’s credit ratings or any current or future criteria or models used in the ratings process for credit portfolios or any type of financial security.