Consistent information multivariate density optimizing methodology

The estimation of the profit and loss distribution of a loan portfolio requires the modelling of the portfolio’s multivariate distribution. This describes the joint likelihood of changes in the credit-risk quality of the loans that make up the portfolio. A significant problem for portfolio credit risk measurement is the greatly restricted data that are available for its modelling. Under these circumstances, convenient parametric assumptions are frequently made in order to represent the nonexistent information. Such assumptions, however, usually do not appropriately describe the behaviour of the assets that are the subject of our interest, loans granted to small and medium enterprises (SMEs), unlisted and arm’s-length firms. This paper proposes the Consistent Information Multivariate Density Optimizing Methodology (CIMDO), based on the cross-entropy approach, as an alternative to generate probability multivariate densities from partial information and without making parametric assumptions. Using the probability integral transformation criterion, we show that the distributions recovered by CIMDO outperform distributions that are used for the measurement of portfolio credit risk of loans granted to SMEs, unlisted and arm’s-length firms.