Computation of credit portfolio loss distribution by a cross entropy method

Abstract

Quantification and management of credit risk is always crucial for the financial industry. Computing credit risk is generally a challenging task while correlated defaults exist. Traditional approaches such as exponential twisting are model specific and often involve difficult analysis, therefore computational methods are sought to estimate the credit risk when analysis is unavailable. The accurate measurement of credit risk is often a rare-event simulation problem, i.e., calculating probabilities (which are usually small) of extreme losses. It is well-known that the Monte Carlo (MC) method may become slow and expensive for such problems. Importance sampling (IS), a variance-reduction technique, can then be utilized for rare-event simulation for credit risk management. In this work, we propose the implementation of a special IS procedure, the cross-entropy (CE) method, to simulate credit risk models. More specifically, we obtain iteratively biasing probability density functions (PDF’s) for credit portfolio losses by the CE method, and then combine the results from each stage by the technique of multiple importance sampling to obtain a complete PDF. The main advantage of this method is that it can avoid the nontrivial analysis required by a general IS method, and therefore simplifies the estimation of loss distributions. Moreover, this approach is generic and can be applied to a wide variety of models with little modifications. In particular, we apply this approach to a normal copula model and a t-copula model to estimate the probabilities of extreme portfolio losses under the models. Numerical examples are provided to demonstrate the performance of our method.