# Credit risk prediction using support vector machines

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## Abstract

The main purpose of this paper is to examine the relative performance between least-squares support vector machines and logistic regression models for default classification and default probability estimation. The financial ratios from a data set of more than 78,000 financial statements from 2000 to 2006 are used as default indicators. The main focus of this paper is on the influence of small training samples and high variance of the financial input data and the classification performance measured by the area under the receiver operating characteristic. The resolution and the reliability of the predicted default probabilities are evaluated by decompositions of the Brier score. It is shown that support vector machines significantly outperform logistic regression models, particularly under the condition of small training samples and high variance of the input data.

## Keywords

Support vector machines Credit risk prediction Default classification Estimation of probabilities of default Training sample size Accounting data## JEL Classification

C14 G33## References

- Abe S (2005) Support vector machines for pattern classification. Springer, LondonGoogle Scholar
- Atiya AF (2001) Bankruptcy prediction for credit risk using neural networks: a survey and new results. IEEE Trans Neural Netw 12(4):929–935CrossRefGoogle Scholar
- Baesens B, van Gestel T, Viaene S, Stepanova M, Suykens JAK, Vanthienen J (2003) Benchmarking state-of-the-art classification algorithms for credit scoring. J Oper Res Soc 54:627–635CrossRefGoogle Scholar
- Bamber D (1975) The area above ordinal dominance graph and the area below the receiver operating characteristic graph. J Math Psychol 12:387–415CrossRefGoogle Scholar
- Basel Committee on Banking Supervision (2006) International convergence of capital measurement and capital standards. Bank for International Settlements, BaselGoogle Scholar
- Boser BE, Guyon IM, Vapnik VN (1992) A traininig algorithm for optimal margin classifers. In: Haussler D (ed) Proceedings of the 5th annual ACM workshop on computational learning theory. ACM Press, New York, pp 144–152CrossRefGoogle Scholar
- Butera G, Faff R (2006) An integrated multi-model credit rating system for private firms. Rev Quantitat Finance Account 26:311–340CrossRefGoogle Scholar
- Carling K, Jacobson T, LindT J, Roszbach K (2007) Corporate credit risk modeling and the macroeconomy. J Bank Finance 31(3):845–868CrossRefGoogle Scholar
- Chen LH, Chiou TW (1999) A fuzzy credit-rating approach for commercial loans: a taiwan case. Omega 27:407–419CrossRefGoogle Scholar
- Chen S, Härdle W, Moro R (2006) Estimation of default probabilities with support vector machines. Discussion Paper 77, SFB 649 Humboldt University, BerlinGoogle Scholar
- Cortes C, Vapnik VN (1995) Support-vector networks. Mach Learn 20(3):273–297Google Scholar
- Cristianini N, Shawe-Taylor J (2006) An introduction to support vector machines. Cambridge University Press, CambridgeGoogle Scholar
- DeLong ER, DeLong DM, Clarke-Pearson DL (1988) Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach. Biometrics 44:837–845CrossRefGoogle Scholar
- Engelmann B, Hayden E, Tasche D (2003) Testing rating accuracy. Risk pp 82–86Google Scholar
- Evgeniou T, Pontil M, Poggio T (2000) Regularization networks and support vector machines. Adv Comput Math 13:1–50CrossRefGoogle Scholar
- Hastie T, Tibshirani R (1990) Generalized additive models. Chapmann and Hall, LondonGoogle Scholar
- Hastie T, Tibshirani R, Friedman J (2001) The elements of statistical learning: data mining, inference, and prediction. Springer, New YorkGoogle Scholar
- Hersbach H (2000) Decomposition of the continuous ranked probability score for ensemble prediction systems. Am Meteorol Soc 15:559–570Google Scholar
- Hosmer DW, Lemeshow S (2000) Applied logistic regression, 2nd edn. Wiley, New YorkCrossRefGoogle Scholar
- Huang Z, Chen H, Hsu CJ, Chen WH, Wu S (2004) Credit rating analysis with support vector machines and neural networks: a market comparative study. Decis Support Syst 37:543–558CrossRefGoogle Scholar
- Härdle W, Moro R, SchSfer D (2005) Predicting bankcruptcy with support vector machines. In: Cizek P, Härdle W, Weron R (eds) Statistical tools for finance and insurance. Springer, Berlin, pp 225–248CrossRefGoogle Scholar
- Härdle W, Lee YJ, SchSfer D, Yeh YR (2007) The default risk of firms examined with smooth support vector machines. Discussion Paper 757, DIW BerlinGoogle Scholar
- McLachlan GJ (2004) Discriminant analysis and statistical pattern recognition. Wiley, New YorkGoogle Scholar
- Ravi Kumar P, Ravi V (2007) Bankcruptcy prediction in banks and firms via statistical and inteligent techniques—a review. Eur J Oper Res 180:1–28CrossRefGoogle Scholar
- Schölkopf B, Smola AJ (2002) Learning with kernels. MIT Press, CambridgeGoogle Scholar
- Sun L (2007) A re-evaluation of auditors’ opinions versus statistical models in bankruptcy prediction. Rev Quantitat Finance Account 28:55–78CrossRefGoogle Scholar
- Suykens JA, Vandewalle J (1999) Least squares support vector machine classifiers. Neural Process Lett 9:293–300CrossRefGoogle Scholar
- Suykens JA, van Gestel T, Brabanter JD, Moor BD, Vandewalle J (2002) Least squares support vector machines. World Scientific, SingaporeCrossRefGoogle Scholar
- Theodoridis S, Koutroumbas K (2006) Pattern recognition. Elsevier Academic Press, AmsterdamGoogle Scholar
- van Gestel T, Suykens JA, Baesens B, Viaene S, Vanthienen J, Dedene G, de Moor Joss Vandewalle B (2004) Benchmarking least squares support vector machine classifiers. Mach Learn 54:5–32CrossRefGoogle Scholar
- Vapnik VN (1998) Statistical learning theory. Wiley, New YorkGoogle Scholar
- Vapnik VN (2000) The nature of statistical learning theory, 2nd edn. Springer, BerlinGoogle Scholar
- Varetto F (1998) Genetic algorithms applications in the analysis of insolvency risk. J Bank Finance 22:1421–1439CrossRefGoogle Scholar
- Yobas MB, Crook JN, Ross P (2000) Credit scoring using neural and evolutionary techniques. IMA J Manage Math 11(2):111–125CrossRefGoogle Scholar