Evaluation of Credit Risk Under Correlated Defaults: The Cross-Entropy Simulation Approach

Credit risk, associated to borrowers defaulting on their debts, is an ever growing source of concern for lenders. The presence of correlation among defaults may be described by the t-copula model. However, the typically large number of variables involved calls for a simulation approach. A simulation method, based on the use of the Cross-Entropy (CE) technique, is here proposed as an alternative to non-adaptive Importance Sampling (IS) techniques so far presented in the literature, the main advantage of CE being that it allows to deal easily with a wider range of probability models than ad hoc IS. The method is validated through a comparison of its results with the crude MonteCarlo and the Exponential Twist approaches. The proposed Cross-Entropy technique is shown to provide accurate results even when the sample size is several orders of magnitude smaller than the inverse of the probability to be estimated.