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Single Asset Constant Geometric Brownian Motion Baseline Stress Testing With Seasonality


Author: Anthony, C.*, Odu-Ndom N.K and Amadi, I.U
Department of Mathematics/Statistics Ignatius Ajuru University of Education, Rumuolumeni, Port Harcourt.
Published Date: 2026-10-09
Keywords: Stochastic processes, Bank, GBM, Exponential Decay and Seasonal effect.
Abstract:

This study models a distressed bank under Central Bank of Nigeria (CBN) regulatory pressure where baseline valuation decays exponentially with multiplicative seasonality effect. Three analytical paths and theoretical expected means were simulated showing up and down horizontal trend lines instead of exponential growth. Sensitivity analysis for volatility and drift shows both plots look alike with up and down horizontal movements, unlike growth banks where volatility dominates. Results show distressed pattern trapped sideways oscillation with slow decay, indicating that both growth rate and volatility cannot rescue the bank under regulatory overhang. Implication is range-bound trading rather than buy-and-hold. This system is valuable for regulators and risk managers.