Credit Risk Calculation: An Application in the Brazilian Market Using the CreditRisk+ Model with Uncertainties

Due to an increasing economic instability worldwide, financial institutions are demanding more robust and powerful methodologies of credit risk modeling in order to ensure their financial health. The statistical model CreditRisk+, developed by Credit Suisse Financial Products (CSFP), is widely spread in the insurance market since it is not necessary to make assumptions. This is because the model is based on the default risk, that is, non-payment risk. The main goal of the above-mentioned model is to measure expected and non-expected losses in a credit portfolio. In order to measure default events, the model suggests grouping the debtors in exposure ranges so that the loss distribution can be approached to a Poisson. In the basic model, the default rates are fixed. To portray reality, we propose a new modeling in which the uncertainties and volatilities of default rates are incorporated. In this case, a new model which assumes a Gamma distribution in association with these uncertainties is defined. From the obtained distribution, not only is it possible to calculate the credit VaR (Value-at-Risk) but also the loss distribution and some point estimates, such as the expected loss in a certain period of time and the economic capital allocation. The main goal of this article is the CreditRisk+ model application with uncertainties in a segment of Brazilian industry. The economic capital allocation, that is, the difference between VaR and the expected deprival value is always higher, depending on the proposed modeling (with the incorporation of uncertainties, volatilities and the default rates). Our result is important, since financial institutions can be underestimating their losses in stressful moments.