Bayesian Approach to PD Calibration and Stress-testing in Low Default Portfolios

Standard approach to low default portfolio (LDP) probability of default (PD) calibration is to add conservative add-on that should cover the gap with scarce default event data. The most prominent approaches to add-on calibration are based on an assumption about the level of the conservatism (quantile of default event distribution), but there is no transparent way to calibrate it or to relate the level of conservatism to a risk profile of the Bank. Over conservative assumptions can lead to undue shrinkage in LDP and negative shift in the overall risk-profile. Described in the paper PD calibration framework is based on Bayesian inference. The main idea is to calibrate conjugate prior using “closest†available portfolio (CPP) with reliable default statistics. The form of the prior, criteria for CPP selection, application of the approach to real life and artificial portfolios are described in the paper. The advantage of the approach is an elimination of the arbitrary “level of conservatism assumption†. The level of conservatism is transparently restricted by CPP portfolio, the general principle is the more data one have for LDP portfolio, the less weight model puts on CPP risk profile. Proposed approach could be also extended for stress-testing purposes.JEL classification numbers: C01Keywords: probability of default, credit risk, PD calibration, stress-testing