This system presents the classical Geometric Brownian Motion (GBM) benchmark with constant initial price. The Stochastic Differential Equation (SDE) assumes no deterministic trend, seasonality or regime effects. The simulation results for Fidelity Bank share prices were presented using a constant GBM model with varying sample paths. Four graphical solutions were analyzed to examine path behavior, expected growth, and sensitivity to drift and volatility. The results highlight the interaction between deterministic trend and stochastic noise in shaping Fidelity’s price dynamics. The model serves as a benchmark for market efficiency with no deterministic trend. Also, the existence and uniqueness of the strong solution is proved under standard Lipschitz conditions. This system serves as the null model for comparing the other stochastic systems.