Extreme value theory is the study of extremal properties of random processes, it models and measures events that occur with little probability. The extreme value theory is a robust framework to analyze the tail behavior of distributions. It has been applied extensively in hydrology, climatology, insurance and finance industry. The information of probability of customer default is very useful while analyzing the credit risks in banks. Logistic regression model has been used extensively to model the probability of loan defaults. However, it has some limitations when it comes to modeling rare events, for example, the underestimation of the default probability which could be very risky for the bank. The second limitation/drawback is that the logit link is symmetric about 0.5, this means that the response curve п(x i) approaches one at the same rate it approaches zero. To overcome these limitations the study sought to implement regression method for binary data based on extreme value theory. The objective of the study was to model loan defaults in Kenya banks using the GEV regression model. The results of GEV were compared with the results of the logistic regression model. The study found out for rare events such as loan defaults the GEV performed better than the logistic regression model. As the percentage of defaulters in a sample became smaller the GEV model to identify defaults improves whereas the logistic regression model becomes poorer.
| Published in | Science Journal of Applied Mathematics and Statistics (Volume 4, Issue 6) |
| DOI | 10.11648/j.sjams.20160406.17 |
| Page(s) | 289-297 |
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
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Copyright © The Author(s), 2024. Published by Science Publishing Group |
Logistic, Generalized Extreme Value Regression, Extreme Value Theory, Confusion Matrix
| [1] | Andrew, C. (2004). Basel II: The reviewed framework of June 2004. Geneva, Switzerland. |
| [2] | Agresti, A. (2002). An introduction to categorical data analysis. New York: Wiley. |
| [3] | Anatoly B. J (2014). The probability of default models of Russian banks. Journal of Institute of Economics in Transition 21 (5), 203-278. |
| [4] | Adrea Ruth.(2010). Measuring the likelihood of small Business default; Journal of Applied Sciences 33 (7), 1289-1386. |
| [5] | Altman E.(1968). Financial ratios, discriminant analysis, and prediction of corporate bankruptcy. Journal of Finance 23 (4) 589-609. |
| [6] | Alexander B.(2012) Determinant of bank failures the case of Russia, Journal of Applied Statistics, 78 (32), 235-403. |
| [7] | Beirlant, (2004). Statistics of extremes. Hoboken, NJ: Wiley. |
| [8] | Calabrese, R. (2012). Modelling SME loan defaults as rare events: The generalized extreme value regression. Journal Of Applied Statistics, 00 (00), 1-17. |
| [9] | Calabrese R. (2011). Generalized extreme value regression for binary rare events data: an application to credit default. Journal of Applied Statistics, 2 (4), 4-8. |
| [10] | Castillo, E. (2005). Extreme value and related models with applications in engineering and science. Hoboken, N. J.: Wiley. |
| [11] | Coles, S. (2001). An introduction to statistical modeling of extreme values. London: Springer. |
| [12] | David (1977). Early warning of bank failure: A logit regression approach. Journal of Banking and Finance, 19, 109-301. |
| [13] | Dobson A. J (2002). An Introduction to Generalized linear models. 2nd ed. Boca rayon. |
| [14] | Eliason, S. R (1993) Maximum Likelihood Estimation: Logic and Practice. Sage University Paper series on Quantitative Application in social sciences, series no. 07-096. Newbury Park. |
| [15] | Falk, M., Hüsler, J. & Reiss, R. (1994). Laws of small numbers: extremes and rare events; [based on lectures given at the DMV Seminar on "Laws of small numbers; extremes and rare events," held at the Katholische UniversitätEichstätt from October 20 - 27, 1991]. Basel [u.a.]: Birkhäuser. |
| [16] | Galambos, J. (1978). The asymptotic theory of extreme order statistics. New York: Wiley. |
| [17] | Gilli, M., &Këllezi, E. (2000). Extreme value theory for tail-related risk measures. Geneva: FAME. |
| [18] | Goodhart, C. (2011). The Basel Committee on Banking Supervision. Cambridge: Cambridge University Press. |
| [19] | Gumbel, E. (1958). Statistics of extremes. New York: Columbia University Press. |
| [20] | Haan, L., & Ferreira, A. (2006). Extreme value theory. New York: Springer. |
| [21] | Haotian chen and Ziyuan Chen. Data mining on loan Default prediction. Journal of Institute of Economics in Transition 214 (7), 256-298. |
| [22] | Jenkison, (1956). Statistics of extremes. Hoboken, NJ: Wiley. |
| [23] | Junjie Liang (2013) Predicting borrowers chance of defaulting on credit loans. American Journal of Theoretical and Applied Statistics, 1345 (2), 4556-4598. |
| [24] | Leadbetter, M., Lindgren, G., &RootzeÌn, H. (1983). Extremes and related properties of random sequences and processes. New York: Springer-Verlag. |
| [25] | Leadbetter, M., Lindgren, G., &Rootzen, H. (1980). Extremal and Related Properties of Stationary Processes. Part II. Extreme Values in Continuous Time. Ft. Belvoir: Defense Technical Information Center. |
| [26] | Lenntand Golet (2014). Symmetric and asymmetric binary choice models for corporate bankruptcy, Journal of social and behavior sciences, 124 (14), 282-291. |
| [27] | McCullagh P., Nelder J. A (1989) Generalized linear model, Chapman Hall, Newyork. |
| [28] | O. Adem., & Waititu, A. (2012). Parametric modeling of the probability of bank loan default in Kenya. Journal of Applied Statistics, 14 (1), 61-74. |
| [29] | Oliveira, J. (1984). Statistical Extremes and Applications. Dordrecht: Springer Netherlands. |
| [30] | Omkar G. (2002). Predicting loan defaults. American Journal of Theoretical and Applied Statistics, 15 (3), 3543-3789. |
| [31] | Rafaella, C. Giampiero, M. Bankruptcy Prediction of small and medium enterprises using s flexible binary GEV extreme value model. American Journal of Theoretical and Applied Statistics, 1307 (2), 3556-3798. |
| [32] | Paul Embrechts, Resnick, Sydney. (1987). Extreme values, regular variation, and point processes. New York: Springer-Verlag. |
| [33] | Semmes, T. (2011). Gumbel. Newyork. |
| [34] | Sjur Westgaard (2002). Capital Structure and the prediction of bankruptcy. American Journal of applied statistics, 45 (57), 543-678. |
| [35] | Singhee, A., & Rutenbar, R. (2010). Extreme statistics in nanoscale memory design. New York: Springer. |
| [36] | Uday Rajan (2010). Statistical models and incentives, Journal of Applied Sciences, 100 (2) 3456-3500 |
| [37] | Von Mises, (1936). Theory of Statistics of extremes. Hoboken, NJ: Wiley. |
| [38] | Wikipedia, (2015). Generalized extreme value distribution. Retrieved 2 December 2015, from http://en.wikipedia.org/wiki/Extreme_value_distribution |
APA Style
Stephen Muthii Wanjohi, Anthony Gichuhi Waititu, Anthony Kibira Wanjoya. (2016). Modeling Loan Defaults in Kenya Banks as a Rare Event Using the Generalized Extreme Value Regression Model. Science Journal of Applied Mathematics and Statistics, 4(6), 289-297. https://doi.org/10.11648/j.sjams.20160406.17
ACS Style
Stephen Muthii Wanjohi; Anthony Gichuhi Waititu; Anthony Kibira Wanjoya. Modeling Loan Defaults in Kenya Banks as a Rare Event Using the Generalized Extreme Value Regression Model. Sci. J. Appl. Math. Stat. 2016, 4(6), 289-297. doi: 10.11648/j.sjams.20160406.17
AMA Style
Stephen Muthii Wanjohi, Anthony Gichuhi Waititu, Anthony Kibira Wanjoya. Modeling Loan Defaults in Kenya Banks as a Rare Event Using the Generalized Extreme Value Regression Model. Sci J Appl Math Stat. 2016;4(6):289-297. doi: 10.11648/j.sjams.20160406.17
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Download@article{10.11648/j.sjams.20160406.17,
author = {Stephen Muthii Wanjohi and Anthony Gichuhi Waititu and Anthony Kibira Wanjoya},
title = {Modeling Loan Defaults in Kenya Banks as a Rare Event Using the Generalized Extreme Value Regression Model},
journal = {Science Journal of Applied Mathematics and Statistics},
volume = {4},
number = {6},
pages = {289-297},
doi = {10.11648/j.sjams.20160406.17},
url = {https://doi.org/10.11648/j.sjams.20160406.17},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20160406.17},
abstract = {Extreme value theory is the study of extremal properties of random processes, it models and measures events that occur with little probability. The extreme value theory is a robust framework to analyze the tail behavior of distributions. It has been applied extensively in hydrology, climatology, insurance and finance industry. The information of probability of customer default is very useful while analyzing the credit risks in banks. Logistic regression model has been used extensively to model the probability of loan defaults. However, it has some limitations when it comes to modeling rare events, for example, the underestimation of the default probability which could be very risky for the bank. The second limitation/drawback is that the logit link is symmetric about 0.5, this means that the response curve п(x i) approaches one at the same rate it approaches zero. To overcome these limitations the study sought to implement regression method for binary data based on extreme value theory. The objective of the study was to model loan defaults in Kenya banks using the GEV regression model. The results of GEV were compared with the results of the logistic regression model. The study found out for rare events such as loan defaults the GEV performed better than the logistic regression model. As the percentage of defaulters in a sample became smaller the GEV model to identify defaults improves whereas the logistic regression model becomes poorer.},
year = {2016}
}
TY - JOUR T1 - Modeling Loan Defaults in Kenya Banks as a Rare Event Using the Generalized Extreme Value Regression Model AU - Stephen Muthii Wanjohi AU - Anthony Gichuhi Waititu AU - Anthony Kibira Wanjoya Y1 - 2016/11/16 PY - 2016 N1 - https://doi.org/10.11648/j.sjams.20160406.17 DO - 10.11648/j.sjams.20160406.17 T2 - Science Journal of Applied Mathematics and Statistics JF - Science Journal of Applied Mathematics and Statistics JO - Science Journal of Applied Mathematics and Statistics SP - 289 EP - 297 PB - Science Publishing Group SN - 2376-9513 UR - https://doi.org/10.11648/j.sjams.20160406.17 AB - Extreme value theory is the study of extremal properties of random processes, it models and measures events that occur with little probability. The extreme value theory is a robust framework to analyze the tail behavior of distributions. It has been applied extensively in hydrology, climatology, insurance and finance industry. The information of probability of customer default is very useful while analyzing the credit risks in banks. Logistic regression model has been used extensively to model the probability of loan defaults. However, it has some limitations when it comes to modeling rare events, for example, the underestimation of the default probability which could be very risky for the bank. The second limitation/drawback is that the logit link is symmetric about 0.5, this means that the response curve п(x i) approaches one at the same rate it approaches zero. To overcome these limitations the study sought to implement regression method for binary data based on extreme value theory. The objective of the study was to model loan defaults in Kenya banks using the GEV regression model. The results of GEV were compared with the results of the logistic regression model. The study found out for rare events such as loan defaults the GEV performed better than the logistic regression model. As the percentage of defaulters in a sample became smaller the GEV model to identify defaults improves whereas the logistic regression model becomes poorer. VL - 4 IS - 6 ER -
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