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Mixture cure models in credit scoring: If and when borrowers default


  • Tong, Edward N.C.
  • Mues, Christophe
  • Thomas, Lyn C.


Mixture cure models were originally proposed in medical statistics to model long-term survival of cancer patients in terms of two distinct subpopulations – those that are cured of the event of interest and will never relapse, along with those that are uncured and are susceptible to the event. In the present paper, we introduce mixture cure models to the area of credit scoring, where, similarly to the medical setting, a large proportion of the dataset may not experience the event of interest during the loan term, i.e. default. We estimate a mixture cure model predicting (time to) default on a UK personal loan portfolio, and compare its performance to the Cox proportional hazards method and standard logistic regression. Results for credit scoring at an account level and prediction of the number of defaults at a portfolio level are presented; model performance is evaluated through cross validation on discrimination and calibration measures. Discrimination performance for all three approaches was found to be high and competitive. Calibration performance for the survival approaches was found to be superior to logistic regression for intermediate time intervals and useful for fixed 12month time horizon estimates, reinforcing the flexibility of survival analysis as both a risk ranking tool and for providing robust estimates of probability of default over time. Furthermore, the mixture cure model’s ability to distinguish between two subpopulations can offer additional insights by estimating the parameters that determine susceptibility to default in addition to parameters that influence time to default of a borrower.

Suggested Citation

  • Tong, Edward N.C. & Mues, Christophe & Thomas, Lyn C., 2012. "Mixture cure models in credit scoring: If and when borrowers default," European Journal of Operational Research, Elsevier, vol. 218(1), pages 132-139.
  • Handle: RePEc:eee:ejores:v:218:y:2012:i:1:p:132-139
    DOI: 10.1016/j.ejor.2011.10.007

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    References listed on IDEAS

    1. Yildiray Yildirim, 2008. "Estimating Default Probabilities of CMBS Loans with Clustering and Heavy Censoring," The Journal of Real Estate Finance and Economics, Springer, vol. 37(2), pages 93-111, August.
    2. Thomas J. Steichen & Nicholas J. Cox, 2002. "A note on the concordance correlation coefficient," Stata Journal, StataCorp LP, vol. 2(2), pages 183-189, May.
    3. Thomas, Lyn C., 2009. "Modelling the credit risk for portfolios of consumer loans: Analogies with corporate loan models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(8), pages 2525-2534.
    4. Thomas, Lyn C., 2009. "Consumer Credit Models: Pricing, Profit and Portfolios," OUP Catalogue, Oxford University Press, number 9780199232130.
    5. Crook, Jonathan N. & Edelman, David B. & Thomas, Lyn C., 2007. "Recent developments in consumer credit risk assessment," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1447-1465, December.
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    Cited by:

    1. Alexandre, Michel & Antônio Silva Brito, Giovani & Cotrim Martins, Theo, 2017. "Default contagion among credit modalities: evidence from Brazilian data," MPRA Paper 76859, University Library of Munich, Germany.
    2. Bravo, Cristián & Maldonado, Sebastián & Weber, Richard, 2013. "Granting and managing loans for micro-entrepreneurs: New developments and practical experiences," European Journal of Operational Research, Elsevier, vol. 227(2), pages 358-366.
    3. Lützenkirchen, Kristina & Rösch, Daniel & Scheule, Harald, 2014. "Asset portfolio securitizations and cyclicality of regulatory capital," European Journal of Operational Research, Elsevier, vol. 237(1), pages 289-302.
    4. Lessmann, Stefan & Baesens, Bart & Seow, Hsin-Vonn & Thomas, Lyn C., 2015. "Benchmarking state-of-the-art classification algorithms for credit scoring: An update of research," European Journal of Operational Research, Elsevier, vol. 247(1), pages 124-136.
    5. repec:pal:jorsoc:v:68:y:2017:i:6:d:10.1057_s41274-016-0128-9 is not listed on IDEAS
    6. Peter-Hendrik Ingermann & Frederik Hesse & Christian Bélorgey & Andreas Pfingsten, 2016. "The recovery rate for retail and commercial customers in Germany: a look at collateral and its adjusted market values," Business Research, Springer;German Academic Association for Business Research, vol. 9(2), pages 179-228, August.
    7. repec:prg:jnlaop:v:2018:y:2018:i:1:id:594:p:34-46 is not listed on IDEAS
    8. Perko, Igor, 2017. "Behaviour-based short-term invoice probability of default evaluation," European Journal of Operational Research, Elsevier, vol. 257(3), pages 1045-1054.
    9. Wolter, Marcus & Rösch, Daniel, 2014. "Cure events in default prediction," European Journal of Operational Research, Elsevier, vol. 238(3), pages 846-857.
    10. repec:gam:jsusta:v:9:y:2017:i:10:p:1834-:d:114674 is not listed on IDEAS
    11. Liu, Fan & Hua, Zhongsheng & Lim, Andrew, 2015. "Identifying future defaulters: A hierarchical Bayesian method," European Journal of Operational Research, Elsevier, vol. 241(1), pages 202-211.
    12. Akkoç, Soner, 2012. "An empirical comparison of conventional techniques, neural networks and the three stage hybrid Adaptive Neuro Fuzzy Inference System (ANFIS) model for credit scoring analysis: The case of Turkish cred," European Journal of Operational Research, Elsevier, vol. 222(1), pages 168-178.
    13. Lee, Yongwoong & Rösch, Daniel & Scheule, Harald, 2016. "Accuracy of mortgage portfolio risk forecasts during financial crises," European Journal of Operational Research, Elsevier, vol. 249(2), pages 440-456.
    14. He, Ping & Hua, Zhongsheng & Liu, Zhixin, 2015. "A quantification method for the collection effect on consumer term loans," Journal of Banking & Finance, Elsevier, vol. 57(C), pages 17-26.
    15. Dirick, Lore & Claeskens, Gerda & Baesens, Bart, 2015. "An Akaike information criterion for multiple event mixture cure models," European Journal of Operational Research, Elsevier, vol. 241(2), pages 449-457.
    16. Tong, Edward N.C. & Mues, Christophe & Brown, Iain & Thomas, Lyn C., 2016. "Exposure at default models with and without the credit conversion factor," European Journal of Operational Research, Elsevier, vol. 252(3), pages 910-920.
    17. Mariusz Górajski & Dobromił Serwa & Zuzanna Wośko, 2016. "Measuring expected time to default under stress conditions for corporate loans," NBP Working Papers 237, Narodowy Bank Polski, Economic Research Department.


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