Modeling loan default in Zimbabwe microfinance sector using Jump-Diffusion dynamics and Azuma-Hoeffding concentration bounds.

Abstract

This study develops and validates a jump diffusion model with Azuma-Hoeffding inequality for the modelling of loan default risk for the microfinance sector in Zimbabwe. The inadequacy of existing credit risk models for the country is the motivating factor for the development of this model. Data obtained from the Zimbabwe Reserve Bank and ZIMSTATS time series databases for the period between 2015Q1 and 2025Q4 is used to develop the model. The data consists of 44 observations for the measurement of Portfolio at Risk for loans defaulting greater than 30 days (PaR>30 days), inflation rates, lending rates, and exchange rate volatility. The parameters of the jump diffusion model were estimated using maximum likelihood estimation and structural breaks were detected using the Bai-Perron test for structural changes in time series data. Model validation used the Root Mean Square Error (RSME), Mean Absolute Error (MAE), Akaike Information Criterion (AIC) and tail coverage rate of one thousand simulated model paths using the Euler-Maruyama method. The descriptive statistics of the loan default risk variables all exhibit a positive skewness and non-normal distribution, demonstrating the unstable nature of the Zimbabwean economy. The estimation of the jump diffusion model parameter indicates that there is moderate volatility in the loan defaults with jumps in the number of default loans observed; two jump events were identified in the period that correspond to the 2019 currency reform and the 2023-2024 ZiG Transition. Four regimes of default loans were identified using the Bai-Perron test indicating changes in the average number of default loans within the country over the study period that correlated with economic shocks to the nation. The validation measures for the jump diffusion model indicated that it outperformed both the diffusion model alone and the ARIMA model in forecasting the number of default loans in the country, and it was able to fully capture all the jumps in the default loans within the period studied. Thus, the model developed for the determination of loan default risk in the microfinance sector in Zimbabwe exhibits stochastic jumps in loan defaults that are caused by macroeconomic shocks to the economy of Zimbabwe. The model can be utilized by the microfinance institutions in the country to improve the management of their loans and the credit risk within their portfolios.