Credit Risk Prediction based on Bayesian estimation of logistic regression model with random effects

Mestiri, Sami and Farhat, Abdejelil (2018): Credit Risk Prediction based on Bayesian estimation of logistic regression model with random effects.

Abstract

The aim of this current paper is to predict the credit risk of banks in Tunisia, over the period (2000-2005). For this purpose, two methods for the estimation of logistic regression model with random effects: Penalized Quasi Likelihood (PQL) method and Gibbs Sampler algorithm are applied. By using information on a sample of 528 Tunisian firms and 26 financial ratios,we show that Bayesian approach improves the quality of model predictions in terms of good classification as well as by the ROC curve result.

• Item Type: MPRA Paper
• Language: English
• Keywords: Forecasting, Credit risk, Penalized Quasi Likelihood, Gibbs Sampler, Logistic regression with random effects, Curve ROC
• Subjects: C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C58 - Financial Econometrics; G - Financial Economics > G2 - Financial Institutions and Services

References

Altman, E. I. (1968). Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. The Journal of Finance, 23.4,589-609.

Avery, R.B., Bostic, R.W., Calem, P.S., and Canner G.B. (2000) Credit Scoring: Statistical Issues and Evidence from Credit-Bureau Files. Real Estate Economics, 28, 523-547

Albert, J. (2007). Bayesian Computation with R. New York: Springer Science+Business Media, LLC.

[ Alfo, M., Caiazza, S. and Trovato, G. (2005),. Extending a Logistic Approach to Risk Modeling through Semiparametric Mixing. Journal of Financial Services Research, vol. 28, no. 1, pp. 163.

Bolstad, W. M. (2004). Introduction to Bayesian statistics. Hoboken, NJ: John Wiley & Sons, Inc.

Breslow, N. and Clayton, D. G. (1993). Approximate Inference in Generalized Linear Mixed Models. Journal American Statistical Society n 88, 9-25.

Fernandes, G. and Rocha, C.A. (2011). Low Default Modelling: A Comparison of Techniques Based on a Real Brazilian Corporate Portfolio.

Hand, D., and Henley, W. (1997), Statistical Classification Methods in Consumer Credit Scoring: A Review. Journal of the Royal Statistical Society A, 160, 523-541.

Mira, A. and Tenconi, P. (2004). Bayesian estimate of credit risk via MCMC with delayed rejection. In: Seminar on Stochastic Analysis, Random Fields and Applications IV. Centro Stefano Franscini, Ascona, pp. 277-291.

Mestiri, S., Hamdi, M.(2012). Credit Risk Prediction: A Comparative Study Between Logistic Regression and Logistic Regression with Random Effects International Journal of Management Science and Engineering Management 7 (3), Taylor & Francis, 200-204.

Hamdi, M., Mestiri, S. (2014). Bankruptcy Prediction For Tunisian Firms: An Application Of Semi-Parametric Logistic Regression and Neural Networks Approach. Economics Bulletin 34 (1), AccessEcon, 133-143.

Laitinen, E.K. (1999) Predicting a Corporate Credit Analyst’s Risk Estimate by Logistic and Linear Models. International Review of Financial Analysis, vol. 8, no. 2, pp. 97.

Steenackers, A. and Goovaerts, M.J. (1989) A Credit Scoring Model for Personal Loans. Insurance Mathematics and Economics, vol. 8, no.1, pp.31.

Loffler, G., Posch, P.N., and Schone, C. (2005). Bayesian methods for improving credit scoring models. Technical report, Department of Finance, University of Ulm, Germany.

Ntzoufras, I. (2009). Bayesian Modeling Using WinBUGS. John Wiley Sons, Inc., Hoboken, New Jersey.

Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2004). Bayesian Data Analysis (2nd ed.). Boca Raton, FL: Chapman & Hall/CRC.

Geman, S., and Geman, D. (1984), Stochastic Relaxation, Gibbs Distributions and the Bayesian Restoration of Images”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.

Gelfand, A.E., and Smith, A.F.M. (1990), Sampling Based Approaches to Calculating Marginal Densities, Journal of the American Statistical Association, 85, 398-409.

Pepe, M. S. (2000). Receiver operating characteristic methodology. Journal of the American Statistical Association, 95 :308-311.

Press, S. J. and Wilson, S. (1978). Choosing between logistic regression and discriminant analysis. Journal of the American Statistical Association,73:699-705.

Thomas, L.C. (2000), A Survey of Credit and Behavioural Scoring: Forecasting Financial Risk of Lending to Consumers. International Journal of Forecasting, vol. 16, no. 2, pp.149.

Wong, G.Y., and Mason, W.M. (1985), The Hierarchical Logistic Regression Model for Multilevel Analysis. Journal of the American Statistical Association, 80, 513-524.

Wylie, J., Muegge, S. and Thomas, D.R. (2006), Bayesian Methods in Management Research: an Application to Logistic Regression

Wilhelmsen, M., Dimakos, X.K., Huseb, T., and Fiskaaen, M. (2009). Bayesian Modelling of Credit Risk using Integrated Nested Laplace Approximations. Available from http://publications.nr.no BayesianCreditRiskUsingINLA.pdf.

Ziemba, A. (2005). Bayesian Updating of Generic Scoring Models.