A dynamic Bayesian approach for probability of default and stress test

Abstract

Obligor defaults are cross-sectionally correlated as obligors share common economic conditions; in addition obligors are longitudinally correlated so that an economic shock like the IMF crisis in 1998 lasts for a period of time. A longitudinal correlation should be used to construct statistical scenarios of stress test with which we replace a type of artificial scenario that the banks have used. We propose a Bayesian model to accommodate such correlation structures. Using 402 obligors to a domestic bank in Korea, our model with a dynamic correlation is compared to a Bayesian model with a stationary longitudinal correlation and the classical logistic regression model. Our model generates statistical financial statement under a stress situation on individual obligor basis so that the genearted financial statement produces a similar distribution of credit grades to when the IMF crisis occurred and complies with Basel IV (Basel Committee on Banking Supervision, 2017) requirement that the credit grades under a stress situation are not sensitive to the business cycle