A Numerical Framework for Forecasting Financial Risk in Microfinance Institutions Using the Fourth-Order Runge-Kutta Method

Abstract

This study proposes a robust numerical model for forecasting financial risk patterns in Microfinance Institutions (MFIs) using the conventional fourth-order Runge-Kutta (RK4) algorithm. As microfinance institutions engage with low-income vulnerable populations, accurate risk prediction has become more crucial due to variable repayment behaviors and external macroeconomic disruptions. Conventional statistical methods often overlook the inherent time-dependent nonlinearities in the evolution of MFI portfolio risk. Conversely, RK4 provides a reliable and computationally efficient framework for solving ordinary differential equations (ODEs) that characterize risk evolution. The principal technique is developing a risk dynamic model concerning loan default probability, repayment rates, and liquidity exposure, discretizing the resultant ordinary differential equations using the RK4 method, and producing forecasts for short to medium time horizons. The model relies on publicly accessible data from the World Bank and the African Development Bank, supported by empirical evidence. Quantitative findings indicate that RK4-based forecasts correctly adhere to empirical risk patterns and reveal hidden patterns that linear models overlook. The framework improves risk assessment procedures in microfinance by offering a mathematically clear, scalable, and computationally efficient forecasting system. This harmonization is strategically important for MFIs' financial planning, promoting stability via preventative measures and consistent operational management. The study identifies a significant gap between actual financial management and applied numerical computation, offering a methodology for hybrid analytic-financial modelling pertinent to microcredit environments.