Abstract
Fierce competition as well as the recent financial crisis in financial and banking industries made credit scoring gain importance. An accurate estimation of credit risk helps organizations to decide whether or not to grant credit to potential customers. Many classification methods have been suggested to handle this problem in the literature. This paper proposes a model for evaluating credit risk based on binary quantile regression, using Bayesian estimation. This paper points out the distinct advantages of the latter approach: that is (i) the method provides accurate predictions of which customers may default in the future, (ii) the approach provides detailed insight into the effects of the explanatory variables on the probability of default, and (iii) the methodology is ideally suited to build a segmentation scheme of the customers in terms of risk of default and the corresponding uncertainty about the prediction. An often studied dataset from a German bank is used to show the applicability of the method proposed. The results demonstrate that the methodology can be an important tool for credit companies that want to take the credit risk of their customer fully into account.
Similar content being viewed by others
References
Alqallaf F and Gustafson P (2001). On cross-validation of Bayesian models. Canadian Journal of Statistics-Revue Canadienne De Statistique 29 (2): 333–340.
Antonietta M and Paolo T (2003). Bayesian estimate of credit risk via MCMC with delayed rejection. Economics and quantitative methods, Department of Economics, University of Insubria.
Arias O, Sosa-Escudero W and Hallock KF (2001). Individual heterogeneity in the returns to schooling: Instrumental variables quantile regression using twins data. Empirical Economics 26 (1): 7–40.
Asuncion A and Newman D (2007). UCI machine learning repository, http://archive.ics.uci.edu/ml/.
Baesens B, Setiono R, Mues C and Vanthienen J (2003a). Using neural network rule extraction and decision tables for credit-risk evaluation. Management Science 49 (3): 312–329.
Baesens B, Van Gestel T, Viaene S, Stepanova M, Suykens J and Vanthienen J (2003b). Benchmarking state-of-the-art classification algorithms for credit scoring. Journal of the Operational Research Society 54 (6): 627–635.
Bajpai N (2009). Business Statistics. Pearson: India.
Bassett Jr. G W and Chen H (2001). Portfolio style: Return-based attribution using quantile regression. Empirical Economics 26 (1): 293–305.
Bayarri M and Berger J (2004). The interplay of Bayesian and frequentist analysis. Statistical Science 19 (1): 58–80.
Bellotti T and Crook J (2009). Support vector machines for credit scoring and discovery of significant features. Expert Systems with Applications 36 (2): 3302–3308.
Benoit DF and Van den Poel D (2009). Benefits of quantile regression for the analysis of customer lifetime value in a contractual setting: An application in financial services. Expert Systems with Applications 36 (7): 10475–10484.
Benoit DF and Van den Poel D (2012). Binary quantile regression: A Bayesian approach based on the asymmetric Laplace distribution. Journal of Applied Econometrics, published online 14 October, doi:10.1002/jae.1216.
Benoit DF, Al-Hamzawi R, Yu K and Van den Poel D (2011). bayesQR: Bayesian quantile regression. R package version 1.3, http://CRAN.R-project.org/package=bayesQR.
Bocker K (2010). Rethinking Risk Measurement and Reporting: Volume II. Risk Books: London.
Bradley AP (1997). The use of the area under the ROC curve in the evaluation of machine learning algorithms. Pattern Recognition 30 (7): 1145–1159.
Buchinsky M (1994). Changes in the US wage structure 1963–1987: Application of quantile regression. Econometrica 62 (2): 405–458.
Buchinsky M (1998). The dynamics of changes in the female wage distribution in the USA: A quantile regression approach. Journal of Applied Econometrics 13 (1): 1–30.
Chamberlain G (1994). Quantile regression, censoring, and the structure of wages. In: Sims C. (ed). Advances in Econometrics—Sixth World Congress. Vol. 1. Cambridge University Press: Cambridge.
Chib S and Greenberg E (1995). Understanding the Metropolis–Hastings algorithm. The American Statistician 49 (4): 327–335.
Engle RF and Manganelli S (2004). CAViaR: Conditional autoregressive value at risk by regression quantiles. Journal of Business & Economic Statistics 22 (4): 367–381.
Fisher R (1936). The use of multiple measurements in taxonomic problems. Annals of Eugenics 7 (2): 179–188.
Galindo J. and Tamayo P. (2000). Credit risk assessment using statistical and machine learning: Basic methodology and risk modeling applications. Computational Economics 15 (1–2): 107–143.
Henley WE and Hand DJ (1996). A k-NEAREST-NEIGHBOUR Classier for assessing consumer credit risk. The Statistician 45 (1): 77.
Ho T (2002). Rule induction in constructing knowledge-based decision support. In: Kersten G, Mikolajuk Z and Yeh A (eds). Decision Support Systems for Sustainable Development. Kluwer Academic Publishers: USA, pp 263–276.
Huang C, Chen M and Wang C (2007). Credit scoring with a data mining approach based on support vector machines. Expert Systems with Applications 33 (4): 847–856.
Jacobs M and Kiefer N (2010). The Bayesian approach to default risk: A guide. In: Böcker K. (ed). Rethinking Risk Measurement and Reporting. Vol. II. Risk Books: London, pp 319–334.
Kahn LM (1998). Collective bargaining and the interindustry wage structure: International evidence. Economica 65 (260): 507–534.
Koenker R and Bassett G (1978). Regression quantiles. Econometrica 46 (1): 33–50.
Kordas G (2002). Credit scoring using binary quantile regression. In: Dodge Y (ed). Statistical Data Analysis Based on the L1-norm and Related Methods. Birkhuser: Basel.
Kordas G (2006). Smoothed binary regression quantiles. Journal of Applied Econometrics 21 (3): 387–407.
Lee T and Chen I (2005). A two-stage hybrid credit scoring model using artificial neural networks and multivariate adaptive regression splines. Expert Systems with Applications 28 (4): 743–752.
Lee T, Chiu C, Lu C and Chen I (2002). Credit scoring using the hybrid neural discriminant technique. Expert Systems with Applications 23 (3): 245–254.
Lewis EM (1994). An Introduction to Credit Scoring. 2nd edn. Athena Press: San Rafael, CA.
Li ML and Miu P (2010). A hybrid bankruptcy prediction model with dynamic loadings on accounting-ratio-based and market-based information: A binary quantile regression approach. Journal of Empirical Finance 17 (4): 818–833.
Maltritz D and Molchanov A (2008). Economic determinants of country credit risk: A Bayesian approach. Proceedings of the 12th New Zealand Finance Colloquium, Palmerston North, NZ: Massey University, 14–15 February.
Manski CF (1975). Maximum score estimation of the stochastic utility model of choice. Journal of Econometrics 3 (3): 205–228.
Martens D, Van Gestel T, De Backer M, Haesen R, Vanthienen J and Baesens B (2009). Credit rating prediction using ant colony optimization. Journal of the Operational Research Society 61 (4): 561–573.
Martin D (1977). Early warning of bank failure: A logit regression approach. Journal of Banking & Finance 1 (3): 249–276.
Mays FE (2004). Credit Scoring for Risk Managers: The Handbook for Lenders. 1st edn. South Western Educational Publishing: United States of America.
McCulloch W and Pitts W (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysic 5 (4): 115–133.
Meinshausen N (2006). Quantile regression forests. Journal of Machine Learning Research 7: 983–999.
Myers RH (2000). Classical and Modern Regression with Applications. 2nd edn. Duxbury Press: Boston.
Neter J, Kutner M, Wasserman W and Nachtsheim C (1996). Applied Linear Statistical Models. 4th edn. McGraw-Hill/Irwin: New York.
Quinlan JR (1986). Induction of decision trees. Machine Learning 1 (1): 81–106.
Quinlan JR (1992). C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers Inc.: California.
Raymond A (2007). The Credit Scoring Toolkit: Theory and Practice for Retail Credit Risk Management and Decision Automation. 1st edn. Oxford University Press: United States of America.
Schebesch K and Stecking R (2005). Support vector machines for credit scoring: Extension to non standard cases. In: Baier D and Wernecke K (eds). Innovations in Classification, Data Science, and Information Systems. Studies in Classification, Data Analysis, and Knowledge Organization, pp. 498–505, Springer: Berlin.
Thomas LC, Edelman DB and Crook JN (2002). Credit Scoring & Its Applications. 1st edn. Society for Industrial Mathematics: Philadelphia.
Thomas LC, Oliver RW and Hand DJ (2005). A survey of the issues in consumer credit modelling research. Journal of the Operational Research Society 56 (9): 1006–1015.
Umantsev L and Chernozhukov V (2001). Conditional value-at-risk: Aspects of modeling and estimation. Empirical Economics 26 (1): 271–292.
Verstraeten G and Van den Poel D (2004). The impact of sample bias on consumer credit scoring performance and profitability. Journal of the Operational Research Society 56 (8): 981–992.
West D, Dellana S and Qian J (2005). Neural network ensemble strategies for financial decision applications. Computers & Operations Research 32 (10): 2543–2559.
Witten IH and Eibe F (2005). Data Mining. Morgan Kaufmann: San Francisco.
Xiao W, Zhao Q and Fei Q (2006). A comparative study of data mining methods in consumer loans credit scoring management. Journal of Systems Science and Systems Engineering 15 (4): 419–435.
Yu K and Zhang J (2005). A three-parameter asymmetric Laplace distribution and its extension. Communications in Statistics: Theory and Methods 34 (9–10): 1867–1879.
Zheng Z (2012). QBoost: Predicting quantiles with boosting for regression and binary classification. Expert Systems with Applications 39 (2): 1687–1697.
Author information
Authors and Affiliations
Corresponding author
Appendix
Appendix
Rights and permissions
About this article
Cite this article
Miguéis, V., Benoit, D. & Van den Poel, D. Enhanced decision support in credit scoring using Bayesian binary quantile regression. J Oper Res Soc 64, 1374–1383 (2013). https://doi.org/10.1057/jors.2012.116
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1057/jors.2012.116