Paper: arXiv 2403.13192

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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"]

Cited References (13)

  1. A methodology for stochastic analysis of share prices as Markov chains with finite states (2014)
  2. Comparing South African financial markets behaviour to the Geometric Brownian motion process (2008)
  3. A review on Geometric Brownian Motion in forecasting the share prices in Bursa Malaysia (2012)
  4. Continuous Time Processes in Times of Crisis: The Case Of GBM and CEV Models (2011)
  5. Development of modified geometric Brownian motion models by using stock price data and basic statistics (2009)
  6. Analysis of financial time series (2005)
  7. Option pricing when underlying stock returns are discontinuous (1976)
  8. Stock price modelling: Theory and Practice (2006)
and 5 more
  1. Determining the return volatility of the Ghana stock exchange before and during the COVID-19 pandemic using the exponential GARCH model (2022)
  2. Poisson Process Modeling of Pure Jump Equities on the Ghana Stock Exchange (2022)
  3. Exchange Rate and Stock Price Nexus: Evidence from Ghana (2021)
  4. Bayesian Switching Volatility Models for Analysing Stock Returns in Ghana (2022)
  5. Drivers of stock prices in Ghana: an empirical mode decomposition approach (2021)

0 of 13 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.