Using multi-state markov models to identify credit card risk
Régis, Daniel Evangelista; Artes, Rinaldo
http://dx.doi.org/10.1590/0103-6513.160814
Production, vol.26, n2, p.330-344, 2016
Abstract
The main interest of this work is to analyze the application of multi-state Markov models to evaluate credit card risk by investigating the characteristics of different state transitions in client-institution relationships over time, thereby generating score models for various purposes. We also used logistic regression models to compare the results with those obtained using multi-state Markov models. The models were applied to an actual database of a Brazilian financial institution. In this application, multi-state Markov models performed better than logistic regression models in predicting default risk, and logistic regression models performed better in predicting cancellation risk.
Keywords
Credit scoring. Survival analysis. Multi-state Markov models. Credit cards. Markov processes.
References
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Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd ed.). New York: John Wiley & Sons.
Hosmer, D. W., Lemeshow, S., & May, S. (2008). Applied survival analysis: regression modeling of time to event data (2nd ed.). Hoboken: John Wiley & Sons.
Hougaard, P. (1999). Multi-state models: a review. Lifetime Data Analysis, 5(3), 239-264. http://dx.doi.org/10.1023/A:1009672031531. PMid:10518372.
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Kay, R. (1986). A Markov model for analysing cancer markers and disease states in survival studies. Biometrics, 42(4), 855-865. http://dx.doi.org/10.2307/2530699. PMid:2434150.
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Kuhn, I. N. (2009). Administração financeira de negócio. Ijuí: Editora Ijuí.
Lewis, E. M. (1992). An introduction to credit scoring (2nd ed.). San Rafael: Athena Press.
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Menard, S. (2010). Logistic regression: from introductory to advanced concepts and applications. Los Angeles: Sage Publications Inc.
Montgomery, D. C., & Peck, E. A. (1992). Introduction to linear regression analysis (2nd ed.). New York: John Wiley & Sons.
Paes, A. T., & Lima, A. C. (2004). A SAS macro for estimating transition probabilities in semiparametric models for recurrent events. Computer Methods and Programs in Biomedicine, 75(1), 59-65. http://dx.doi.org/10.1016/j.cmpb.2003.08.007. PMid:15158048.
R Core Team (2014). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved in 4 November 2014, from http://www.R-project.org/
So, M. M. C., & Thomas, L. C. (2010). Modeling and model validation of the impact of the economy on the credit risk of credit card portfolios. The Journal of Risk Model Vaidation, 4, 93-126.
Thomas, L. C. (2000). A survey of credit and behavioural scoring: forecasting financial risk of lending to consumers. International Journal of Forecasting, 16(2), 149-172. http://dx.doi.org/10.1016/S0169-2070(00)00034-0.
Thomas, L. C. (2009). Consumer credit models: pricing, profit and portfolio. Oxford: Oxford Press.
Thomas, L. C., Edelman, D. B., & Crook, J. N. (2002). Credit scoring and its applications. Philadelphia: Siam.
Thomas, L. C., Ho, J., & Scherer, W. T. (2001). Time will tell: behavior scoring and the dynamics of consumer credit assessment. IMA Journal of Management Mathematics, 12(1), 89-103. http://dx.doi.org/10.1093/imaman/12.1.89.
Thomas, L. C., Oliver, R. W., & Hand, D. J. (2005). A survey of the issues in consumer credit modelling research. The Journal of the Operational Research Society, 56(9), 1006-1015. http://dx.doi.org/10.1057/palgrave.jors.2602018.
Trench, M. S., Pederson, S. P., Lau, E. T., Ma, L., Wang, H., & Nair, S. K. (2003). Managing credit lines and prices for Bank One credit cards. Interfaces, 33(5), 4-21. http://dx.doi.org/10.1287/inte.33.5.4.19245.
Van den Poel, D., & Larivière, B. (2004). Customer attrition analysis for financial services using proportional hazard models. European Journal of Operational Research, 157(1), 196-217. http://dx.doi.org/10.1016/S0377-2217(03)00069-9.
Wang, H. Y. F., & Ikeda, A. A. (2004). Análise do mercado de cartão de crédito brasileiro. São Paulo: FEAUSP. Retrieved in 30 January 2015, from http://www.ead.fea.usp.br/Semead/7semead/paginas/artigos%20recebidos/marketing/mkt09-_analise_de_mercado_do_cartao_de_cr%E9dito.pdf
Andreeva, G. (2006). European generic scoring models using survival analysis. The Journal of the Operational Research Society, 57(10), 1180-1187. http://dx.doi.org/10.1057/palgrave.jors.2602091.
Araujo, E. A., & Carmona, C. U. M. (2007). Desenvolvimento de Modelos Credit Scoring com Abordagem de Regressão de Logística para a Gestão da Inadimplência de uma Instituição de Microcrédito. Contabilidade Vista & Revista, 3, 107-131.
Blackwell, M., & Sykes, C. (1992). The assignment of credit limits with a behavior-scoring system. IMA Journal of Management Mathematics, 4(1), 73-80. http://dx.doi.org/10.1093/imaman/4.1.73.
Chi, B.-W., & Hsu, C.-C. (2012). A hybrid approach to integrate genetic algorithm into dual scoring model in enhancing the performance of credit scoring model. Expert Systems with Applications, 39(3), 2650-2661. http://dx.doi.org/10.1016/j.eswa.2011.08.120.
Cox, D. R., & Miller, H. D. (1965). The theory of stochastic processes. London: Chapman and Hall.
David, W. H., Stanley, L., & Susanne, M. (2008). Applied survival analysis: regression modeling of time to event data (2nd ed.). New York: John Wiley & Sons.
Finlay, S. (2010). Credit scoring, response, modelling and insurance rating: a practical guide to forecasting consumer behavior. London: Palgrave Macmillan.
Gupta, J., Wilson, N., Gregoriou, A., & Healy, J. (2014). The effect of internalization on modelling credit risk for SMEs: evidence from UK market. Journal of International Financial Markets, Institutions and Money, 31, 397-413. http://dx.doi.org/10.1016/j.intfin.2014.05.001.
Hoper, M. A., & Lewis, E. M. (1992). Behavior scoring and adaptive control systems. In L. C. Thomas, J. N. Crook & D. B. Edelman (Orgs.), Credit scoring and credit control (pp. 257-276). Oxford: Claredon Press.
Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd ed.). New York: John Wiley & Sons.
Hosmer, D. W., Lemeshow, S., & May, S. (2008). Applied survival analysis: regression modeling of time to event data (2nd ed.). Hoboken: John Wiley & Sons.
Hougaard, P. (1999). Multi-state models: a review. Lifetime Data Analysis, 5(3), 239-264. http://dx.doi.org/10.1023/A:1009672031531. PMid:10518372.
Jackson, C. H. (2007). Multi-state modeling with R: the MSM package version 0.6. London: Imperial College. Retrieved in 16 July 2013, from http://rss.acs.unt.edu/Rdoc/library/msm/doc/msm-manual.pdf
Jackson, C. H., Sharpless, L. D., Thompson, S. G., Duffy, S. W., & Couto, E. (2003). Multistate markov models for disease progression with classification error. The Statistician, 52(2), 193-209. http://dx.doi.org/10.1111/1467-9884.00351.
Kalbfleisch, J. D., & Lawless, J. F. (1985). The analysis of panel data under a markov assumption. Journal of the American Statistical Association, 80(392), 863-871. http://dx.doi.org/10.1080/01621459.1985.10478195.
Kay, R. (1986). A Markov model for analysing cancer markers and disease states in survival studies. Biometrics, 42(4), 855-865. http://dx.doi.org/10.2307/2530699. PMid:2434150.
King, G., & Zeng, L. (2001). Logistic Regression in Rare Events Data. Political Analysis, 9(2), 137-163. http://dx.doi.org/10.1093/oxfordjournals.pan.a004868.
Kuhn, I. N. (2009). Administração financeira de negócio. Ijuí: Editora Ijuí.
Lewis, E. M. (1992). An introduction to credit scoring (2nd ed.). San Rafael: Athena Press.
Marshall, G., & Jones, R. H. (1995). Multi-state models and diabetic retinopathy. Statistics in Medicine, 14(18), 1975-1983. http://dx.doi.org/10.1002/sim.4780141804. PMid:8677398.
Menard, S. (2010). Logistic regression: from introductory to advanced concepts and applications. Los Angeles: Sage Publications Inc.
Montgomery, D. C., & Peck, E. A. (1992). Introduction to linear regression analysis (2nd ed.). New York: John Wiley & Sons.
Paes, A. T., & Lima, A. C. (2004). A SAS macro for estimating transition probabilities in semiparametric models for recurrent events. Computer Methods and Programs in Biomedicine, 75(1), 59-65. http://dx.doi.org/10.1016/j.cmpb.2003.08.007. PMid:15158048.
R Core Team (2014). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved in 4 November 2014, from http://www.R-project.org/
So, M. M. C., & Thomas, L. C. (2010). Modeling and model validation of the impact of the economy on the credit risk of credit card portfolios. The Journal of Risk Model Vaidation, 4, 93-126.
Thomas, L. C. (2000). A survey of credit and behavioural scoring: forecasting financial risk of lending to consumers. International Journal of Forecasting, 16(2), 149-172. http://dx.doi.org/10.1016/S0169-2070(00)00034-0.
Thomas, L. C. (2009). Consumer credit models: pricing, profit and portfolio. Oxford: Oxford Press.
Thomas, L. C., Edelman, D. B., & Crook, J. N. (2002). Credit scoring and its applications. Philadelphia: Siam.
Thomas, L. C., Ho, J., & Scherer, W. T. (2001). Time will tell: behavior scoring and the dynamics of consumer credit assessment. IMA Journal of Management Mathematics, 12(1), 89-103. http://dx.doi.org/10.1093/imaman/12.1.89.
Thomas, L. C., Oliver, R. W., & Hand, D. J. (2005). A survey of the issues in consumer credit modelling research. The Journal of the Operational Research Society, 56(9), 1006-1015. http://dx.doi.org/10.1057/palgrave.jors.2602018.
Trench, M. S., Pederson, S. P., Lau, E. T., Ma, L., Wang, H., & Nair, S. K. (2003). Managing credit lines and prices for Bank One credit cards. Interfaces, 33(5), 4-21. http://dx.doi.org/10.1287/inte.33.5.4.19245.
Van den Poel, D., & Larivière, B. (2004). Customer attrition analysis for financial services using proportional hazard models. European Journal of Operational Research, 157(1), 196-217. http://dx.doi.org/10.1016/S0377-2217(03)00069-9.
Wang, H. Y. F., & Ikeda, A. A. (2004). Análise do mercado de cartão de crédito brasileiro. São Paulo: FEAUSP. Retrieved in 30 January 2015, from http://www.ead.fea.usp.br/Semead/7semead/paginas/artigos%20recebidos/marketing/mkt09-_analise_de_mercado_do_cartao_de_cr%E9dito.pdf
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