Stress Testing and Model Validation: Application of the Bayesian Approach to a Credit Risk Portfolio

Journal of Risk Model Validation, 2015, Vol. 9(3), 41-70

Posted: 1 Nov 2015

See all articles by Michael Jacobs

Michael Jacobs

Accenture Consulting

Ahmet K Karagozoglu

Hofstra University, Zarb School of Business

Frank Sensenbrenner

Johns Hopkins University - Paul H. Nitze School of Advanced International Studies (SAIS)

Date Written: October 30, 2015

Abstract

Following the recent global financial crisis, regulators have recognized the importance of stress testing, in part due to the impact of model risk, and have implemented supervisory requirements in both the revised Basel framework and the Comprehensive Capital Analysis and Review (CCAR) program. We contribute to the literature by developing a Bayesian-based credit risk stress-testing methodology, which can be implemented by small-to-medium-sized banks, as well as presenting empirical results using data from the recent CCAR implementations. Through the application of a Bayesian model, we can formally incorporate exogenous scenarios and also quantify the uncertainty in model output that results from stochastic model inputs. We contribute to the model validation literature by comparing the proportional model risk buffer measure of the severely adverse cumulative nine-quarter loss estimate – a common way to estimate, being a measure of statistical uncertainty generated by a model – obtained from our empirical implementation of the Bayesian to the frequentist model. We find it to be 40% higher in the former than in the latter. As for the model validation exercise, the Bayesian model outperforms the frequentist model statistically significantly, according to the cumulative percentage error metric, by 2% (1.5%) over the entire sample (downturn period).

Keywords: stress testing; model validation; model risk; credit risk; Bayesian analysis; CCAR

Suggested Citation

Jacobs, Michael and Karagozoglu, Ahmet K and Sensenbrenner, Frank, Stress Testing and Model Validation: Application of the Bayesian Approach to a Credit Risk Portfolio (October 30, 2015). Journal of Risk Model Validation, 2015, Vol. 9(3), 41-70. Available at SSRN: https://ssrn.com/abstract=2684227

Michael Jacobs (Contact Author)

Accenture Consulting ( email )

1345 Avenue of the Americas
New York, NY 10105
United States
9173242098 (Phone)

Ahmet K Karagozoglu

Hofstra University, Zarb School of Business ( email )

Department of Finance
134 Hofstra University
Hempstead, NY 11549
United States
(516) 463-5701 (Phone)
(718) 701-8331 (Fax)

HOME PAGE: http://people.hofstra.edu/ahmet_k_karagozoglu/

Frank Sensenbrenner

Johns Hopkins University - Paul H. Nitze School of Advanced International Studies (SAIS) ( email )

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