Estimating Unbiassed Expected Loss, with Application to Consumer Credit

Abstract

The credit risk measure, Expected Loss (EL) is defined as the product of the three risk parameters: probability of default (PD), loss given default (LGD) and exposure at default (EAD). EL is central to risk management, profit estimation, calculating regulatory capital requirements and the standard accounting rules for credit (IFRS 9). Although correlations between the three risk parameters is evident, there is limited published work exploring these correlations and their impact on estimating EL accurately and without bias. Often EL is calculated simply assuming independence. In this study, EL is derived from first principles, without assuming independence between the three risk parameters. The main results are, firstly, that correlation between PD and LGD has no consequence on the calculation of EL, if LGD is treated as conditional on default. However, correlation between LGD and EAD does have an impact, requiring an adjustment to enable an accurate and unbiassed estimate. Additionally, there is no selection bias resulting from using LGD and EAD models built conditional on default, when applied across the total credit population. These results are demonstrated through a simulation study and by application to a real credit card data set.