Abstract
Credit risk modeling techniques become mature over more than a half century of developments. While modeling for credit risk could be traced back much earlier, theoretical affirmation of statistical models, for example, the multinomial logit model as a special case of the more general conditional logit model, was first provided about a half century ago (McFadden, 1974) using the random utility maximization paradigm. Since then, statistical models like the generalized linear models (GLM) have become the most popular selection in modeling credit risks, though machine learning models start to challenge that dominance in some areas in recent years. Figure 3.1 outlines the structure of various models discussed in this chapter.
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Notes
- 1.
McFadden, D. (1974): “Conditional Logit Analysis of Qualitative Choice Behavior,” in P. Zarembka, (ed.), Frontiers in Econometrics, New York: Academic Press, 105–142.
- 2.
Definition of observations separation and overlap:
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Complete separation: ∃a vector b that correctly allocates all observations to their response groups, i.e.:
$$ \left\{{\displaystyle \begin{array}{cc}{b}^{\prime }{x}_i>0& {y}_i=1\\ {}{b}^{\prime }{x}_i<0& {y}_i=0\end{array}}\right. $$ -
Quasi-complete Separation: ∃a vector b such that:
$$ \left\{{\displaystyle \begin{array}{cc}{b}^{\prime }{x}_i\ge 0& {y}_i=1\\ {}{b}^{\prime }{x}_i\le 0& {y}_i=0\end{array}}\right. $$with equality holds for at least one point
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Overlap: Neither complete separation nor quasi-complete separation.
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- 3.
Kalbfleisch, J. D. and Prentice, R. L. (1980), The Statistical Analysis of Failure Time Data, New York: John Wiley & Sons.
- 4.
Meeker, W. Q. and Escobar, L. A. (1998), Statistical Methods for Reliability Data, New York: John Wiley & Sons.
- 5.
Breiman, L., Friedman, J., Olshen, R. and Stone, C. (1984). Classification and Regression Trees, Wadsworth, New York.
- 6.
Efron, B. (1979). Bootstrap methods: another look at the jackknife, Annals of Statistics 7: 1–26.
- 7.
Breiman, L. (2001). Random forests, Machine Learning 45: 5–32.
- 8.
Hastie, T., Tibshirani, R., & Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction. 2nd ed. New York: Springer.
- 9.
McFadden, D. (1974): “Conditional Logit Analysis of Qualitative Choice Behavior,” in P. Zarembka, (ed.), Frontiers in Econometrics, New York: Academic Press, 105–142.
- 10.
R. L. Prentice, J. D. Kalbfleisch, A. V. Peterson, Jr., N. Flournoy, V. T. Farewell, N. E. Breslow. (1978). “The Analysis of Failure Times in the Presence of Competing Risks.” Biometrics, Vol. 34, No. 4, pp. 541–554.
Judith E. Singer and John B. Willett. (1993). “It’s About Time: Using Discrete-Time Survival Analysis to Study Duration and the Timing of Events.” Journal of Educational Statistics, Vol. 18, No. 2, pp. 155–195.
- 11.
Recoveries from sale of collateral to third party, net of escrow expenses.
- 12.
A credit to the account post charge-off.
- 13.
Net of sales commissions due to the outside collection agencies.
- 14.
Tobin, J., (1958). Estimation of relationship for limited dependent variables. Econometrica 26, 24–36.
- 15.
Ferrari SLP, Cribari-Neto F. (2004). “Beta Regression for Modelling Rates and Proportions.” Journal of Applied Statistics, 31(7), 799–815.
- 16.
Papke, L.E. and Wooldridge, J.M. (1996), “Econometric methods for fractional response variables with an application to 401(k) plan participation rates,” Journal of Applied Econometrics, 11(6), 619–632.
- 17.
Gouriéroux, C., Monfort, A. and Trognon, A. (1984), “Pseudo maximum likelihood methods: applications to Poisson models,” Econometrica, 52(3), 701–720.
- 18.
SIFMA/BMA, Standard Formulas for the Analysis of Mortgage-Backed Securities and Other Related Securities. Uniform Practices/Standard Formulas. Feb 1, 1999.
- 19.
Moral, G. (2011), EAD Estimates for Facilities with Explicit Limits. Chapter 11 in The Basel II Risk Parameters: Estimation, Validation, Stress Testing – with Applications to Loan Risk Management. (eds.) Evelyn Hayden, Daniel Porath, Bernd Engelmann, Robert Rauhmeier. Springer-Verlag Berlin Heidelberg.
- 20.
Akaike, H. (1974), “A New Look at the Statistical Model Identification,” IEEE Transactions on Automatic Control, 19, 716–723.
- 21.
Schwarz, G. (1978), “Estimating the Dimension of a Model,” Annals of Statistics, 6, 461–464.
- 22.
Chen, C. (1993). “Mean Loss of Prediction and Its Asymptotic Unbiased Estimators.” MS Thesis. Institute of Systems Science, Academia, China.
- 23.
Larson, S. C. (1931). “The Shrinkage of the Coefficient of Multiple Correlation.” J. Educ. Psychol. 22, 25–55.
Horst, P. (1941). “Prediction of Personal Adjustment.” New York: Social Science Research Council (Bulletin 48).
- 24.
Stone, M. (1974a). “Cross-Validatory Choice and Assessment of Statistical Predictions.” (With discussion) J. R. Statist. Soc. B 36,111–147.
Stone, M. (1974b). “Cross-Validation and Multinomial prediction.” Biometrika 61, 509–515.
Stone, M. (1977a). “Asymptotics for and against Cross-Validation.” Biometrika 64, 29–35.
Stone, M. (1977b). “An Asymptotic Equivalence of Choice of Model by Cross-Validation and Akaike’s criterion.” J. R. Statist. Soc. B 39, 44–47.
- 25.
Geisser, S. (1974). “A Predictive Approach to the Random Effect Model.” Biometrika 61, 101–107.
Geisser, S. (1975). “The Predictive Sample Reuse Method with Applications.” JASA. 70, 320–328.
- 26.
Chen, C. and Zhang, YG. (2000). “Variable Selection of Structural Models.” Proceedings of World Multiconference on Systemics, Cybernetics, and Informatics, Vol. 8, 769–773.
- 27.
D. Kwiatkowski, P. C. B. Phillips, P. Schmidt, and Y. Shin (1992): “Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root.” Journal of Econometrics 54, 159–178.
- 28.
G. M. Ljung and G. E. P. Box (1978). “On a Measure of a Lack of Fit in Time Series Models.” Biometrika. 65 (2): 297–303.
- 29.
White, H. (1980). “A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity.” Econometrica. 48 (4): 817–838.
- 30.
Shapiro, S. S. and Wilk, M. B. (1965). “An analysis of variance test for normality (complete samples).” Biometrika. 52 (3–4): 591–611.
- 31.
Chen C., Chock D. and Winkler S.L. (1999). “A Simulation Study of Confounding in Generalized Linear Models for Air Pollution Epidemiology.” Environmental Health Perspectives, Vol. 107, 217–222.
References
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19, 716–723.
Breiman, L. (2001). Random forests. Machine Learning, 45, 5–32.
Breiman, L., Friedman, J., Olshen, R., & Stone, C. (1984). Classification and regression trees. Wadsworth.
Chen, C. (1993). Mean loss of prediction and its asymptotic unbiased estimators, MS Thesis, Institute of Systems Science, Academia, China.
Chen, C., & Zhang, Y. G. (2000). Variable selection of structural models. Proceedings of World Multiconference on Systemics, Cybernetics, and Informatics, 8, 769–773.
Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1–26.
Geisser, S. (1974). A predictive approach to the random effect model. Biometrika, 61, 101–107.
Geisser, S. (1975). The predictive sample reuse method with applications. JASA, 70, 320–328.
Gouriéroux, C., Monfort, A., & Trognon, A. (1984). Pseudo maximum likelihood methods: Applications to Poisson models. Econometrica, 52(3), 701–720.
Hastie, T., Tibshirani, R., & Friedman, J. H. (2009). The elements of statistical learning: Data mining, inference, and prediction (2nd ed.). Springer.
Kalbfleisch, J. D., & Prentice, R. L. (1980). The statistical analysis of failure time data. Wiley.
McFadden, D. (1974). Conditional logit analysis of qualitative choice behavior. In P. Zarembka (Ed.), Frontiers in econometrics. Academic Press.
Meeker, W. Q., & Escobar, L. A. (1998). Statistical methods for reliability data. Wiley.
Moral, G. (2011). EAD estimates for facilities with explicit limits. Chapter 11. In E. Hayden, D. Porath, B. Engelmann, & R. Rauhmeier (Eds.), The Basel II risk parameters: Estimation, validation, stress testing - with applications to loan risk management. Springer-Verlag.
Papke, L. E., & Wooldridge, J. M. (1996). Econometric methods for fractional response variables with an application to 401(k) plan participation rates. Journal of Applied Econometrics, 11(6), 619–632.
Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461–464.
Stone, M. (1974a). Cross-Validatory Choice and Assessment of Statistical Predictions (With discussion). Journal of the Royal Statistical Society Series B, 36, 111–147.
Stone, M. (1974b). Cross-validation and multinomial prediction. Biometrika, 61, 509–515.
Stone, M. (1977a). Asymptotics for and against cross-validation. Biometrika, 64, 29–35.
Stone, M. (1977b). An asymptotic equivalence of choice of model by cross-validation and Akaike’s criterion. Journal of the Royal Statistical Society Series B, 39, 44–47.
Tobin, J. (1958). Estimation of relationship for limited dependent variables. Econometrica, 26, 24–36.
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Chen, C. (2024). Credit Modeling Techniques. In: Practical Credit Risk and Capital Modeling, and Validation. Management for Professionals. Springer, Cham. https://doi.org/10.1007/978-3-031-52542-1_3
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