Reducing Estimation Risk Using a Bayesian Approach: Application to Stress Testing Mortgage Loan Default

31 Pages Posted: 29 Oct 2019

See all articles by Zheqi Wang

Zheqi Wang

University of Edinburgh - Edinburgh Business School

Jonathan N. Crook

University of Edinburgh - Business School

Galina Andreeva

University of Edinburgh - Business School

Date Written: July 23, 2019

Abstract

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

Suggested Citation

Wang, Zheqi and Crook, Jonathan N. and Andreeva, Galina, Reducing Estimation Risk Using a Bayesian Approach: Application to Stress Testing Mortgage Loan Default (July 23, 2019). Available at SSRN: https://ssrn.com/abstract=3471529

Zheqi Wang (Contact Author)

University of Edinburgh - Edinburgh Business School ( email )

29 Buccleuch Pl
Edinburgh, Scotland EH8 9JS
United Kingdom

Jonathan N. Crook

University of Edinburgh - Business School ( email )

University of Edinburgh
29 Buccleuch Place
Edinburgh, Scotland EH8 9JS
United Kingdom

Galina Andreeva

University of Edinburgh - Business School ( email )

University of Edinburgh
29 Buccleuch Place
Edinburgh, Scotland EH8 9JS
UNITED KINGDOM

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