Bayesian Multi-Period Model for Assessing Credit Loss Distributions vs. Basel II Model

Abstract

The New Basel Capital Accord (Basel II) developed by the Basel Committee on Banking Supervision establishes new procedures for assessing a credit risk and capital adequacy requirements. For corporate client Basel II model suggests that a bank and its supervisor determine four parameters and substitute them in formulae represented in the model to calculate required capital and risk-weighted assets. Three of four parameters - Maturity, Loss Given Default, Exposure at Default - are characteristics of loan and only one - Probability of a client's default within one year (PD) - is characteristic of a borrower. It is interesting to know whether the single parameter PD (and rules of its processing) can fully and adequately describe defaulting borrower and his inherent risk. To answer this question the current paper develops an alternative Bayesian Multi-period (BMP) model that much more closely traces financial process of lending and its risks. The alternative model has the same output as the Basel II model and quite natural inputs. Both models were tested on the same input data; it was found that their outputs drastically differ from each other. Natural conclusion is that the only parameter PD in Basel II is insufficient characteristic of corporate client's risk. Furthermore, detailed analysis excites strong suspicion that errors are present in mathematical inference of principal Basel II formulae, related to credit risk. Being improved the formulae become much more simple, transparent and to some degree trivial. Some parameters like Probability of Default, Maturity Adjustment need to be redefined while others, like Correlation, appear to be irrelevant within current Basel II model. The Bayesian Multi-period model is proposed as the alternative to the current BaseI II model.