Reducing Estimation Risk Using a Bayesian Approach: Application to Stress Testing Mortgage Loan Default
31 Pages Posted: 29 Oct 2019
Date Written: July 23, 2019
We propose a new stress testing method to model both macroeconomic stress and coefficient uncertainty. 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 parameter posterior distribution obtained in the Bayesian approach to simulating the Bayesian estimated DR distribution, we reduce the estimation risk coming from employing point estimates in stress testing. We find that the simulated DR distribution obtained using the Bayesian approach with the parameter posterior distribution has a standard deviation 1.7 times as large as that using the frequentist approach with parameter mean estimates. Moreover, the 95% and 99% values at risk (VaR) using the Bayesian posterior distribution approach are around 2 times the VaRs at the same probability levels using the point estimate approach.
Keywords: OR in banking, Stress testing, Estimation risk, Bayesian simulation, Probability of default
JEL Classification: G21, G01, C11, E37, C53
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