Comparative analysis of the frequentist and Bayesian approaches to stress testing
Stress testing is necessary for banks as it is required by the Basel Accords for loss predictions and regulatory and economic capital computations. It has become increasingly important especially after the 2008 global financial crisis. Credit models are essential in controlling credit risk. The search for new ways to more accurately predict credit risk continues. This thesis concentrates on stress testing the probability of default using the Bayesian posterior distribution to incorporate estimation uncertainty and parameter instability. It also explores modelling the probability of default using Bayesian informative priors to enhance the model predictive accuracy. A new Bayesian informative prior selection method is proposed to include additional information to credit risk modelling and improve model performances. We employ cross-sectional logistic regressions to model the probability of default of mortgage loans using both the Bayesian approach with various priors and the frequentist approach. In the Bayesian informative prior selection method that we propose, we treat coefficients in the PD model as time series variables. We build ARIMA models to forecast the coefficient values in future time periods and use these ARIMA forecasts as Bayesian informative priors. We find that the Bayesian models using this prior selection method outperform both frequentist models and Bayesian models with other priors in terms of model predictive accuracy. 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 the 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 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 frequentist approach with parameter mean estimates. We furthersimulate DR distributions based on models built on crisis and tranquil time periods to explore the impact changes in model parameters between different scenarios have on stress testing results. We apply the parameter posterior distribution obtained in a Bayesian approach to stress testing to reduce the estimation risk that results from using parameter point estimates. We compute the VaRs and required capital with both parameter instability between scenarios and with estimation risk considered. The results are compared with those obtained when coefficient changes in stress testing models or coefficient uncertainty are neglected. We find that the required capital is considerably underestimated when neither parameter instability nor estimation risk is addressed.