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 |
| Creative Commons |
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), 2016. Published by Science Publishing Group |
Logistic, Generalized Extreme Value Regression, Extreme Value Theory, Confusion Matrix
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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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