Dynamic Forecasting and Risk Analysis of Fidelity Bank’s Stock Prices Using a Time-Inhomogeneous Model

Abstract

This study employs a time-inhomogeneous geometric Brownian motion (GBM) model with time-varying drift µ(t) and volatility σ(t), estimated via a 20-day rolling window on historical log-returns to predict the closing share prices of Fidelity Bank, utilizing historical stock data from January 2019 to December 2024. The model accounts for time-varying drift and volatility, capturing the dynamic behavior of the bank’s stock prices. We conduct a comprehensiverisk analysis, including Value-at-Risk (VaR) and Expected Shortfall (ES), and evaluate forecasting performance using metrics such as Mean Absolute Error (MAE) and Root Mean Squared Error (RMSE). The results demonstrate the model’s ability to effectively capture price trends and volatility, providing robust forecasts and risk estimates. Practical implications for investors and financial analysts are discussed, emphasizing the model’s utility in managing financial risk and informing investment strategies.