Journal of Risk Model Validation

Stress testing and model validation: application of the Bayesian approach to a credit risk portfolio

Michael Jacobs Jr., Ahmet K. Karagozoglu and Frank J. Sensenbrenner

  • Develop a Bayesian credit risk stress testing methodology which can be implemented banks, formally incorporating exogenous scenarios in the Bayesian prior
  • Empirical analysis results using CCAR implementation data to quantify uncertainty in model output resulting from stochastic model inputs.
  • Contribute to model validation literature by comparing proportional model risk buffer measure of the severely adverse cumulative 9-quarter loss estimate
  • Perform model validation of the Bayesian model as compared to the Frequentist model and shows the former to outperform according to a key metric


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).

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