A Probabilistic Approach to Quantify Margin of Conservatism for Data Deficiencies in a Calibration Sample for Credit Scoring Models

Under the advanced internal ratings-based (AIRB) approach, the banks are allowed to use their internally developed models for probability of default (PD), exposure at default (EAD) and loss given default (LGD) parameters. According to the Basel II Accord (2004), the potential over-optimism of such estimates should be mitigated by an additional margin of conservatism (MoC), however, no specific quantification methodology is prescribed. The purpose of this paper is to introduce a novel approach which rigorously quantifies MoC for missing values in a calibration sample for a credit scoring model from a purely probabilistic perspective. We establish a step-wise derivation of the closed-form expression for corresponding MoC and prove that the approach possesses several intuitive statistical properties with respect to the underlying uncertainty. Moreover, the methodology does not rely on a predefined significance level, which is mostly arbitrary in nature, required for various statistical approaches. Finally, the approach can be employed on the client's score level or on the client's factor level with an additional assumption about the interdependence of the risk drivers. The most intuitive dependence structure is also proposed in this paper