Archive
Special Issues

Volume 4, Issue 1, March 2018, Page: 29-37
Modelling Factors Affecting Probability of Loan Default: A Quantitative Analysis of the Kenyan Students' Loan
Pauline Nyathira Kamau, Institute of Mathematical Sciences, Strathmore University, Nairobi, Kenya
Lucy Muthoni, Institute of Mathematical Sciences, Strathmore University, Nairobi, Kenya
Collins Odhiambo, Institute of Mathematical Sciences, Strathmore University, Nairobi, Kenya
Received: Jun. 13, 2018;       Accepted: Jul. 17, 2018;       Published: Aug. 13, 2018
Abstract
In this study, we perform a quantitative analysis of loan applications by computing the probability of default of applicants using information provided in the Kenya Higher Education Loans application forms. We revisit theoretical distributions used in loan defaulters’ analysis particularly, when outliers are significant. Log-logistic, two-parameter Weibull, logistic, log-normal and Burr distribution were compared via simulations. Logistic and log-logistic model performs well under concentrated outliers; a situation that replicates loan defaulters data. We then apply logistic regressions where the binomial nominal variable was defaulter or re-payer, and different factors affecting default probability of a student were treated as independent variables. The resulting models are verified by comparing results of observed data from the Kenyan Higher Education Loans Board.
Keywords
Student Loans, Default Rates, Multiple Logistic Regression
Pauline Nyathira Kamau, Lucy Muthoni, Collins Odhiambo, Modelling Factors Affecting Probability of Loan Default: A Quantitative Analysis of the Kenyan Students' Loan, International Journal of Statistical Distributions and Applications. Vol. 4, No. 1, 2018, pp. 29-37. doi: 10.11648/j.ijsd.20180401.14
Reference
[1]
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 2016; 4(6): 289-297.
[2]
Andrew, C. (2004). Basel II: The reviewed framework of June 2004. Geneva, Switzerland.
[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]
Altman E. (1968). Financial ratios, discriminant analysis, and prediction of corporate bankruptcy. Journal of Finance 23 (4) 589-609.
[5]
Alexander B. (2012) Determinant of bank failures the case of Russia, Journal of Applied Statistics, 78 (32), 235-403.
[6]
Lenntand Golet (2014). Symmetric and symmetric binary choice models for corporate bankruptcy, Journal of social and behavior sciences, 124 (14), 282-291.
[7]
McCullagh P., Nelder J. A (1989) Generalized linear model, Chapman Hall, Newyork.
[8]
O. Adem., & Waititu, A. (2012). Parametric modeling of the probability of bank loan default in Kenya. Journal of Applied Statistics, 14 (1), 61-74.
[9]
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.
[10]
Nick Hillman, Don Hossler, Jacob P. K. Gross & Osman Cekic What Matters in Student Loan Default: A Review of the Research Literature Journal of Student Financial Aid, Issue 1, Article 2, 1-10-2010.
[11]
Blom, Andreas, Reehana Raza, Crispus Kiamba, Himdat Bayusuf, and Mariam Adil. 2016. Expanding Tertiary Education for Well-Paid Jobs: Competitiveness and Shared Prosperity in Kenya. World Bank Studies. Washington, DC: World Bank. Doi: 10.1596/978-1-4648-0848-7. License: Creative Commons Attribution CC BY 3.0 IGO.
[12]
Anamaria Felicia Ionescu The Federal Student Loan Program: Quantitative Implications for College Enrollment and Default Rates Economics Faculty Working Papers, Colgate University Libraries, Summer 6-2008.
[13]
Felicia Ionescu & Nicole Simpson Default Risk and Private Student Loans: Implications for Higher Education Policies Finance and Economics Discussion Series, 2014- 066.
[14]
Michal T. Njenga. The Determinant of Sustainability of Student Loan Schemes: Case Study of Higher Education Loans Board Scool of Business, University of Nairobi, November 2014.
[15]
Mwangi Johnson Muthii Predicting Student’s Loan Default in Kenya: Fisher’s Discriminant Analysis Approach School of Mathematics, University of Nairobi, 2015.
[16]
Emile A. L. J. van Elen Term structure forecasting School of Economics and Management, Tilburg University, 2010.
[17]
Peter C., B. Phillips & Jun Yu Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance Cowles Foundation for Research in Economics, Yale University, University of Auckland and University of York. School of Economics, Singapore Management University, 90 Stamford Road, Singapore 178903.
[18]
Stephen Crowley Maximum Likelihood Estimation of the Negative Binomial Distribution Unpublished Working Paper, 2012.
[19]
Elizabeth Herr & Larry Burt Predicting Student Loan Default for the University of Texas at Austin.
[20]
Christophe Hurlin Maximum Likelihood Estimation and Geometric Distribution Advanced Econometrics, University of Orleans, 2013.
[21]
Mark Huggett, Gustavo Ventura & Amir Yaron Sources of Lifetime Inequality American Economic Review 101, 2923-2954, 2011.
[22]
Stu Field, Parameter Estimation via Maximum Likelihood. Unpublished working paper, 2009.
[23]
Konstantin Kashin Statistical Inference: Maximum Likelihood Estimation. Journal of Finance, spring 2014.
[24]
Littell, R. C., Mc Clave, J. T., & Offen, W. W. (1979). Goodness-of-fit tests for the two parameter Weibull distribution. Communications in Statistics-Simulation and Computation, 8(3), 257-269.
[25]
Limpert, E., & Stahel, W. A. (2017). The log‐normal distribution. Significance, 14(1), 8-9.