Simulation of Correlated Financial Defaults through Smoothed Cross-Entropy

Credit risk, deriving from borrowers defaulting on their debts, represents an ever growing source of concern for financial operators. An established model to describe the associated risk scenario, where correlation among defaults is present, is the t-copula, whose use allows us to evaluate the probability of losses exceeding a given threshold. 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. A full description of the method is provided along with the results obtained for an extended set of model instances. 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.