Volume 4, Issue 6, December 2016, Page: 289-297
Modeling Loan Defaults in Kenya Banks as a Rare Event Using the Generalized Extreme Value Regression Model
Stephen Muthii Wanjohi, Department Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Gichuhi Waititu, Department Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Anthony Kibira Wanjoya, Department Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya
Received: Oct. 4, 2016;       Accepted: Oct. 25, 2016;       Published: Nov. 16, 2016
DOI: 10.11648/j.sjams.20160406.17      View  3231      Downloads  113
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.
Keywords
Logistic, Generalized Extreme Value Regression, Extreme Value Theory, Confusion Matrix
To cite this article
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, Science Journal of Applied Mathematics and Statistics. Vol. 4, No. 6, 2016, pp. 289-297. doi: 10.11648/j.sjams.20160406.17
Copyright
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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