Computational Economics

, Volume 15, Issue 1–2, pp 107–143 | Cite as

Credit Risk Assessment Using Statistical and Machine Learning: Basic Methodology and Risk Modeling Applications

  • J. Galindo
  • P. Tamayo


Risk assessment of financialintermediaries is an area of renewed interest due tothe financial crises of the 1980's and 90's. Anaccurate estimation of risk, and its use in corporateor global financial risk models, could be translatedinto a more efficient use of resources. One importantingredient to accomplish this goal is to find accuratepredictors of individual risk in the credit portfoliosof institutions. In this context we make a comparativeanalysis of different statistical and machine learningmodeling methods of classification on a mortgage loandata set with the motivation to understand theirlimitations and potential. We introduced a specificmodeling methodology based on the study of errorcurves. Using state-of-the-art modeling techniques webuilt more than 9,000 models as part of the study. Theresults show that CART decision-tree models providethe best estimation for default with an average 8.31%error rate for a training sample of 2,000 records. Asa result of the error curve analysis for this model weconclude that if more data were available,approximately 22,000 records, a potential 7.32% errorrate could be achieved. Neural Networks provided thesecond best results with an average error of 11.00%.The K-Nearest Neighbor algorithm had an averageerror rate of 14.95%. These results outperformed thestandard Probit algorithm which attained an averageerror rate of 15.13%. Finally we discuss thepossibilities to use this type of accurate predictivemodel as ingredients of institutional and global riskmodels.


Risk Assessment Training Sample Average Error Modeling Technique Risk Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Adriaans, P. and Zantinge, D. (1996). Knowledge discovery and data mining.Google Scholar
  2. Altman, E., Avery, R.B., Eisenbeis, R.A. and Sinkey, J.F., Jr. (1981). Application of Classification Techniques in Business, Banking and Finance. Jai Press Inc.Google Scholar
  3. Amari, S. (1993). A universal theorem on learning curves. Neural Networks, 6, 161-166.Google Scholar
  4. Amis, E. (1984). Epicurus Scientific Method. Cornell University Press.Google Scholar
  5. Basle Committee on Banking Supervision (1997). Compendium of documents (April) Vol. 2 Advanced supervisory methods, Chapter ll, pp. 82-181.Google Scholar
  6. Berger, J.O. (1985). Statistical Decision Theory and Bayesian Analysis. Springer series in Statistics.Google Scholar
  7. Bigus, J.P. (1996). Data Mining with Neural Networks: Solving Business Problems from Application Development to Decision Support. Google Scholar
  8. Black, F. and Scholes, M.S. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81 (May/June), 637-654.Google Scholar
  9. Blattberg, R.C. and Deighton, J. (1996). Manage marketing by the customer equity test. Harvard Business Review (July/August).Google Scholar
  10. Breeden, D.T. (1979). An intertemporal asset pricing model with stochastic consumption and investment opportunities. Journal of Financial Economics, 7 (September), 265-296. Reprinted in Bhattacharya and Constantinides, eds. (1989).Google Scholar
  11. Breiman, L., Friedman, J.H., Olshen, R.A. and Stone, C.J. (1984). Classification and Regression Trees. Wadsworth Inc., Pacific Glove.Google Scholar
  12. Breiman, L. (1996). Bias, variance, and arcing classifiers. Tech. Rep. 460, Statistics Dept. U. of California, Berkeley (April 1996).Google Scholar
  13. Bourgoin, M. (1994). Applying Machine-Learning Techniques to a Real-World Problem on a Connection Machine CM-5.Google Scholar
  14. Bourgoin, M. and Smith, S. (1995). Leveraging your hidden data to improve ROI: A case study in the credit card business. In Freedman, Klein and Lederman (eds.), Artificial Intelligence in the Capital Markets. Probus Publishing.Google Scholar
  15. Carlin, B.P. and Louis, T.A. (1996). Bayes and Empirical Bayes Methods for Data Analysis. Chapman and Hall.Google Scholar
  16. Cortes, C., Jackel, L.D. and Chiang (1994a). W-P limits on learning machine accuracy imposed by data quality. In G. Tesauro, D.S. Touretzky and T.K. Leen (eds.), Advances in Neural Networks Processing Systems, Vol. 7, p. 239, MIT Press.Google Scholar
  17. Cortes, C., Jackel, L.D., Solla, S.A. and Vapnik, V. (1994b). Learning curves: Asymptotic values and rate of convergence. In G. Tesauro, D.S. Touretzky and T.K. Leen (eds.), Advances in Neural Networks Processing Systems, Vol. 6, p. 327, MIT Press.Google Scholar
  18. Dewatripont, M. and Tirole, J. (1994). The Prudential Regulation of Banks. MIT Press.Google Scholar
  19. Eaton, M.L. (1983). Multivariate Statistics. Wiley, New York.Google Scholar
  20. Elder and Pregibon (1996). A statistical perspective on knowledge discovery in databases. In Advances in Knowledge Discovery and Data Mining. AAAI Press/The MIT Press.Google Scholar
  21. Fayyad, U.M., Piatetsky-Shapiro, G., Smyth, P. and Uthurusamy. R. (eds.) (1996). Advances in Knowledge Discovery and Data Mining. AAAI Press/The MIT Press.Google Scholar
  22. Fletcher, R. (1981). Practical Methods of Optimization. Wiley-Interscience, John Wiley and Sons.Google Scholar
  23. Fisher, R. (1950). Statistical Methods for Research Workers. 11th Edition.Google Scholar
  24. Friedman, J.H., Bentley, J.L. and Finkel, R.A. (1977). An algorithm for finding best matches in logarithmic expected time. ACM Transactions on Mathematical Software, 3, 9-226.Google Scholar
  25. Friedman, J.H. (1997). On bias, variance, 0/1-loss, and the curse of dimensionality. Data Mining and Knowledge Discovery, 1, 55-77.Google Scholar
  26. Freund, Y. and Shapire, R.E. (1995). A decision theoretic generalization on on-line learning and an application to bosting. Computational Learning Theory. 2nd European Conference, EuroCOLT'95, pp. 23-27. Scholar
  27. Fukunaga, K. (1990). Introduction to Statistical Pattern Recognition.Google Scholar
  28. Glymor, C., Madigan, D., Pregibon, D., and Smyth, P. (1997). Statistical themes and lessons for data mining. Data Mining and Knowledge Discovery, 1, 11-28.Google Scholar
  29. Greene, W.H. (1993). Econometric Analysis. Macmillan, 2nd Edition.Google Scholar
  30. Goldberg, D. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley.Google Scholar
  31. Hand, D.J. (1981). Discrimination and Classification. John Wiley, Chichester.Google Scholar
  32. Hassoun, M.H. (1995). Fundamentals of Artificial Neural Networks. MIT Press, Cambridge, Mass.Google Scholar
  33. Horst, R. and Pardalos, P.M. (eds.) (1995). Handbook of Global Optimization. Kluwer.Google Scholar
  34. Hume, D. (1739). An Inquiry Concerning Human Understanding. Prometheus Books, Pub. 1988.Google Scholar
  35. Hutchinson, J.M., Lo, A.W. and Poggio, T. (1994). A non-parametric approach to pricing and hedging derivative securities via learning networks. The Journal of Finance, XLIX (3).Google Scholar
  36. Jaynes, E. (1983). Papers on Probability, Statistics and Statistical Physics. R.D. Rosenkrantz (ed.), D. Reidel Pub. Co.Google Scholar
  37. Jeffreys, H. (1931). Scientific inference. Cambridge Univ. Press.Google Scholar
  38. Kearns, M.J. and Vazirani, U.V. (1994). An Introduction to Computational Learning Theory. MIT Press, Cambridge, Mass.Google Scholar
  39. Keuzenkamp, H.A. and McAleer, M. (1995). Simplicity, scientific inference and econometric modeling. The Economic Journal, 105, 1-21.Google Scholar
  40. Kuan, C.-M. and White, H. (1994). Artificial neural networks: An economic perspective. Econometric Reviews, 13 (1).Google Scholar
  41. Lachenbruch, P.A. and Mickey, M.R. (1968). Discriminant Analysis. Hafner Press, New York.Google Scholar
  42. Landy, A., 1996. A scalable approach to data mining. Informix Tech Notes, 6 (3), 51.Google Scholar
  43. Li, M. and Vitanyi, P. (1997). An Introduction to Kolmogorov Complexity and Its Applications. 2nd Edition, Springer-Verlag, New York.Google Scholar
  44. McClelland, J.L. and Rumelhart, D.E. (eds.) (1986). Parallel Distributed Processing. MIT Press.Google Scholar
  45. McLachan, G.L. (1992). Discriminant Analysis and Statistical Pattern Recognition. John Wiley, New York.Google Scholar
  46. Meyer, P.A. and Pifer, H.W. (1970). Prediction of bank failures. Journal of Finance, 25 (4), 853-868.Google Scholar
  47. Merton, R.C. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4 (Spring), 141-183.Google Scholar
  48. Merton, R.C. (1973). An intertemporal capital asset pricing model. Econometrica, 41 (September), 867-887. Reprinted in Continuous Time Finance (1990). Basil Blackwell as Chapter 15, Cambridge, Mass.Google Scholar
  49. Michie, D., Spiegelhalter, D.J. and Taylor, C.C. (eds.) (1994).Machine learning, neural and statistical classification. Ellis Horwood series in Artificial Intelligence.Google Scholar
  50. Mitchell, T. (1997). Machine Learning. McGraw Hill, tom/mlbook.htmlGoogle Scholar
  51. Opper, M. and Haussler, D. (1995). Bounds for predictive errors in the statistical mechanics of supervised learning. Physical Review Letters, 75, 3772.Google Scholar
  52. Piatetsky-Shapiro, G. and Frawley, W.J. (eds.) (1991). Knowledge Discovery in Databases. MIT Press.Google Scholar
  53. Pindyck, R.S. and Rubinfield, D.L. (1981). Econometric Models and Economic Forecasts. 2nd Edition, McGraw Hill.Google Scholar
  54. Popper, K. (1958). The Logic of Scientific Discovery. Hutchinson & Co, London.Google Scholar
  55. Rissanen, J.J. (1989). Stochastic Complexity and Statistical Inquiry. World Scientific.Google Scholar
  56. Ross, S.A. (1976). Arbitrage theory of capital asset pricing. Journal of Economic Theory, December.Google Scholar
  57. Sharpe, W.F. (1963). A simplified model for portfolio analysis. Management Science, 9 (January), 277-293.Google Scholar
  58. Sinkey, J.F., Jr. (1975). A multivariate statistical analysis on the characteristics of problem banks. Journal of Finance, 30 (1), 21-36.Google Scholar
  59. Simoudis, E., Han, J. and Fayyad U. (eds.) (1996). Proceedings of the Second International Conference on Knowledge Discovery and Data Mining (KDD'96). AAAI Press. See also KDD Nuggets: Small, R.D. and Edelstein, H. (1997). Scalable Data Mining in Building, Using and Managing the Data Warehouse. Prentice Hall PTR.Google Scholar
  60. Stanfill C. and Waltz, D. (1986). Toward memory-based reasoning. CACM, 29, 12l.Google Scholar
  61. Seung, H.S., Sompolinsky, H. and Tishby, N. (1993). Statistical mechanics of learning from examples. Physical Review A, 45, 6056.Google Scholar
  62. Tamayo, P., Berlin, J., Dayanand, N., Drescher, G., Mani, D.R. and Wang. C. (1997). Darwin: An Scalable Integrated System for Data Mining. Thinking Machines white paper.Google Scholar
  63. Wang, C., Venkatesh, S.S. and Judd, J.S. (1994). Optimal stopping and effective machine complexity in learning. In G. Tesauro, D.S. Touretzky and T.K. Leen (eds.), Advances in Neural Networks Processing Systems, 7, 239. MIT Press.Google Scholar
  64. Weiss, S.M. and Kulikowski, C.A. (1991). Computer Systems that Learn: Classification and Prediction Methods from Statistics, Neural Networks, Machine Learning and Expert Systems. Morgan Kaufmann, San Mateo, Calif.Google Scholar
  65. White, H. (1992). Artificial Neural Networks. Blackwell, Cambridge, Mass.Google Scholar
  66. Valiant, L.G. A theory of the learnable. Communications of the ACM, 27, 1134.Google Scholar
  67. Vapnik, V. (1995). The Nature of Statistical Learning Theory. Springer-Verlag.Google Scholar
  68. Zadeh, L.A. (1994). Fuzzy logic, neural networks and soft computing. Communications of the ACM, 3, 77.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • J. Galindo
    • 1
  • P. Tamayo
    • 2
  1. 1.Department of EconomicsHarvard UniversityCambridgeU.S.A.
  2. 2.Thinking Machines Corp.BurlingtonU.S.A.

Personalised recommendations