Modeling stock price dynamics on the Ghana Stock Exchange: A Geometric Brownian Motion approach

ArXiv ID: 2403.13192 “View on arXiv”

Authors: Unknown

Abstract

Modeling financial data often relies on assumptions that may prove insufficient or unrealistic in practice. The Geometric Brownian Motion (GBM) model is frequently employed to represent stock price processes. This study investigates whether the behavior of weekly and monthly returns of selected equities listed on the Ghana Stock Exchange conforms to the GBM model. Parameters of the GBM model were estimated for five equities, and forecasts were generated for three months. Evaluation of estimation accuracy was conducted using mean square error (MSE). Results indicate that the expected prices from the modeled equities closely align with actual stock prices observed on the Exchange. Furthermore, while some deviations were observed, the actual prices consistently fell within the estimated confidence intervals.

Keywords: Geometric Brownian Motion (GBM), Time Series Forecasting, Stock Price Modeling, Mean Square Error (MSE), Equity Analysis, Equities

Complexity vs Empirical Score

• Math Complexity: 6.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper employs advanced mathematical concepts like stochastic differential equations and Itô’s lemma, but its empirical rigor is limited by small sample size (15 equities), lack of robust backtesting, and reliance on simple metrics like MSE without addressing transaction costs or out-of-sample performance beyond a three-month forecast.

  flowchart TD
    A["Research Goal:<br>Do GSE returns conform to GBM?"] --> B["Data Selection<br>Weekly & Monthly Returns<br>5 Selected Equities"]
    B --> C["Parameter Estimation<br>Geometric Brownian Motion<br>Forecast Generation 3 Months"]
    C --> D["Model Evaluation<br>Mean Square Error (MSE)<br>Actual vs Expected Prices"]
    D --> E["Key Findings<br>Prices align with GBM model<br>Actual prices within confidence intervals"]