Reducing estimation risk using a Bayesian posterior distribution approach: Application to stress testing mortgage loan default

We propose a new stress testing method to model coefficient uncertainty in addition to macroeconomic stress. Based on U.S. mortgage loan data, we model the probability of default at account level using discrete time hazard analysis. We employ both the frequentist and Bayesian methods in parameter estimation and default rate (DR) stress testing. By applying the Bayesian parameter posterior distribution, which includes all ranges of possible parameter estimates, obtained in the Bayesian approach to simulating the DR distribution, we reduce the estimation risk coming from employing point estimates in stress testing. Since estimation risk, a commonly neglected source of risk, is addressed in our method, we obtain more prudential forecasts of credit losses. We find that the simulated DR distribution obtained using the Bayesian approach with the parameter posterior distribution has a standard deviation 10.7 times as large as that using the frequentist approach with parameter mean estimates. Moreover, the 99% value at risk (VaR) using the Bayesian posterior distribution approach is around 6.5 times the VaR at the same probability level using the point estimate approach.