A mathematical model for lending in microfinance and applications

Abstract

Loan default is one of the major problems facing most financial institutions. The solution to this problem has been the use of a mathematical model to determine the probability of default of clients of these financial institutions. This study proposes a mathematical model for predicting the probability of default of clients from a microfinance institution. The logistic and survival analysis methods were used in building the model. The results from the logistic regression model showed that the variables Rate, Number of Repayment, Branch Name, Average Inflation Rate and Average Foreign Exchange Rate are significant in predicting the probability of default. The linearity test showed that Number of Repayment was nonlinear and was transformed using restricted cubic splines. The survival analysis model showed that the variables Rate, Product, Branch Name, Easter, New Year, Ramadan, Average Inflation Rate, Average Unemployment Rate, and Average Foreign Exchange Rate were significant in predicting the probability of default of clients. The variables Average Inflation Rate and Average Unemployment Rate were transformed using restricted cubic splines. There also existed interactions between Rate and Product, New Year and Ramadan, and Easter and Average Inflation Rate. The fitted models were evaluated and validated.