Stress Testing Nigerian Banks: An Exponential-Decay Geometric Brownian Motion Model

This paper applies an exponential-decay geometric Brownian motion (GBM) model to illustrate how shocks and sustained downward pressure may affect Nigerian bank stock prices. The standard GBM drift is adjusted from $\mu$ to $\mu-k$, where $k>0$ is the decay rate. Brownian-motion paths illustrate the source of uncertainty, while simulated stock-price paths demonstrate how assets with identical initial values can diverge under volatility. Sensitivity analysis shows that the relationship between $k$ and $\mu$ determines the behavior of the expected price: the mean grows when $\mu>k$, remains constant when $\mu=k$, and declines exponentially when $\mu\mu$, the mean-price half-life is $\ln(2)/(k-\mu)$. The model therefore offers a transparent scenario-generation tool for regulators and risk managers. It is an illustrative stress-testing model rather than an empirically calibrated model of any named Nigerian bank.