Modelling consumer credit risk via survival analysis

  1. Cao Abad, Ricardo
  2. Vilar Fernández, Juan Manuel
  3. Devia Rivera, Andrés
Journal:
Sort: Statistics and Operations Research Transactions

ISSN: 1696-2281

Year of publication: 2009

Volume: 33

Issue: 1

Pages: 3-30

Type: Article

DIALNET GOOGLE SCHOLAR lock_openOpen access editor

More publications in: Sort: Statistics and Operations Research Transactions

Abstract

Credit risk models are used by financial companies to evaluate in advance the insolvency risk caused by credits that enter into default. Many models for credit risk have been developed over the past few decades. In this paper, we focus on those models that can be formulated in terms of the probability of default by using survival analysis techniques. With this objective three different mechanisms are proposed based on the key idea of writing the default probability in terms of the conditional distribution function of the time to default. The first method is based on a Cox's regression model, the second approach uses generalized linear models under censoring and the third one is based on nonparametric kernel estimation, using the product-limit conditional distribution function estimator by Beran. The resulting nonparametric estimator of the default probability is proved to be consistent and asymptotically normal. An empirical study, based on modified real data, illustrates the three methods.

Bibliographic References

  • Allen, L. N. and Rose, L. C. (2006). Financial survival analysis of defaulted debtors, Journal of Operational Research Society, 57, 630-636.
  • Altman, E. I. (1968). Finantial ratios, discriminant analysis, and the prediction of corporate bankruptcy, Journal of Finance, 23, 589-611.
  • Altman, E. I. and Saunders, A. (1998). Credit risk measurement: developments over the last 20 years, Journal of Banking and Finance, 21, 1721-1742.
  • Baba, N. and Goko, H. (2006). Survival analysis of hedge funds, Bank of Japan, Working Papers Series No. 06-E-05.
  • Basel Comitee on Banking Supervison (1999). International convergence of capital measurement and capital standards, Bank for International Settlements.
  • Basel Comitee on Banking Supervision (2004). International convergence of capital measurement and capital standards: a revised framework, Bank for International Settlements.
  • Beran, R. (1981). Nonparametric regression with randomly censored survival data, Unpublished technical report, University of California, Berkeley.
  • Beran, J. and Djaı̈dja, A. K. (2007). Credit risk modeling based on survival analysis with inmunes, Statistical Methodology, 4, 251-276.
  • Carling, K., Jacobson, T. and Roszbach, K. (1998). Duration of consumer loans and bank lending policy: dormancy versus default risk, Working Paper Series in Economics and Finance No. 280, Stockholm School of Economics.
  • Chen, S., Härdle, W. K. and Moro, R. A. (2006). Estimation of default probabilities with support vector machines, Center of Applied Statistics and Economics (CASE), Humboldt-Universität zu Berlin, Germany, SFB 649 discussion paper No. 2006-077.
  • Crouhy, M., Galai, D. and Mark, R. (2000). A comparative analysis of current credit risk models, Journal of Banking and Finance, 24, 59-117.
  • Dabrowska, D. (1987). Non-parametric regression with censored survival time data, Scandinavian Journal of Statistics, 14, 181-197.
  • Dabrowska, D. (1989). Uniform consistency of the kernel conditional Kaplan-Meier estimate, Annals of Statistics, 17, 1157-1167.
  • Fleming, T. R. and Harrington, D. P. (1991). Counting Processes and Survival Analysis, John Wiley & Sons, New York.
  • Glennon, D. and Nigro, P. (2005). Measuring the default risk of small business loans: a survival analysis approach, Journal of Money, Credit, and Banking, 37, 923-947.
  • González-Manteiga, W. and Cadarso-Suárez, C. (1994). Asymptotic properties of a generalized KaplanMeier estimator with some applications, Journal of Nonparametric Statistics, 4, 65-78.
  • Hamerle, A., Liebig, T. and Rösch, D. (2003). Credit risk factor modeling and the Basel II IRB Approach, Deutsche Bundesbank Discussion Paper Series 2, Banking and Financial Supervision, document No. 02/2003.
  • Hand, D. J. (2001). Modelling consumer credit risk, IMA Journal of Management Mathematics, 12, 139- 155.
  • Hanson, S. and Schuermann, T. (2004). Estimating probabilities of default, Federal Reserve Bank of New York, Staff Report No. 190.
  • Iglesias Pérez, M. C. and González-Manteiga, W. (1999). Strong representation of a generalized productlimit estimator for truncated and censored data with some applications, Journal of Nonparametric Statistics, 10, 213-244.
  • Jorgensen, B. (1983). Maximum likelihood estimation and large-sample inference for generalized linear and nonlinear regression models, Biometrika, 70, 19-28.
  • Li, G. and Datta, S. (2001). A bootstrap approach to nonparametric regression for right censored data, Annals of the Institute of Statistical Mathematics, 53, 708-729.
  • Li, G. and Van Keilegom, I. (2002). Likelihood ratio confidence bands in non-parametric regression with censored data, Scandinavian Journal of Statistics, 29, 547-562.
  • Malik, M. and Thomas L. (2006). Modelling credit risk of portfolio of consumer loans, University of Southampton, School of Management Working Paper Series No. CORMSIS-07-12.
  • McCullagh, P. and Nelder, J. A. (1989).Generalized Linear Models , 2nd. Ed., Chapman and Hall, London.
  • Narain, B. (1992). Survival analysis and the credit granting decision. In: Thomas L., Crook, J. N. and Edelman, D. B. (eds.). Credit Scoring and Credit Control. OUP: Oxford, 109-121.
  • Roszbach, K. (2003). Bank lending policy, credit scoring and the survival of loans, Sverriges Riksbank Working Paper Series No. 154.
  • Stepanova, M. and Thomas, L. (2002). Survival analysis methods for personal loan data, Operations Research, 50, 277-289.
  • Saunders, A. (1999). Credit Risk Measurement: New Approaches to Value at Risk and Other Paradigms, John Wiley & Sons, New York.
  • Van Keilegom, I. and Veraverbeke, N. (1996). Uniform strong results for the conditional Kaplan-Meier estimators and its quantiles, Communications in Statistics: Theory and Methods, 25, 2251-2265.
  • Van Keilegom, I., Akritas, M. and Veraverbeke, N. (2001). Estimation of the conditional distribution in regression with censored data: a comparative study, Computational Statistics & Data Analysis, 35, 487-500.
  • Wang, Y., Wang, S. and Lai, K. K. (2005). A fuzzy support vector machine to evaluate credit risk, IEEE Transactions on Fuzzy Systems, 13, 820-831.
Data source: Dialnet