Forecasting Stock Price and Exchange Rate Volatility Using a Comparative Approach of Geometric Brownian Motion and Neural Networks
Keywords:
exchange rate, stock price index volatility, neural network model, Brownian drop motion modelAbstract
This study aims to compare the predictive power of the Geometric Brownian Motion (GBM) model and neural networks in forecasting volatility of Tehran Stock Exchange price index and exchange rate. This applied quantitative study used monthly data of the Tehran Stock Exchange price index and official exchange rate from 2012 to 2023. Volatility presence was first confirmed using the ARCH test. Volatility modeling was then performed using a numerically solved GBM framework based on stochastic differential equations and the Fokker–Planck approach, and its performance was compared with an online-learning neural network model. Model accuracy was evaluated using the coefficient of determination (R²) and root mean squared error (RMSE). For the stock price index, the GBM model achieved R² = 0.5751 and RMSE = 0.059, outperforming the neural network (R² = 0.438; RMSE = 0.448). For the exchange rate, GBM yielded R² = 0.5245 and RMSE = 0.026, compared to R² = 0.410 and RMSE = 0.447 for the neural network. Both research hypotheses were statistically supported, confirming the superior predictive performance of the GBM model. The Geometric Brownian Motion model demonstrates significantly higher predictive accuracy and explanatory power than neural networks in forecasting stock market and exchange rate volatility, offering a more reliable analytical framework for financial forecasting and investment decision-making.
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Copyright (c) 2025 Rouzbeh Zarezadeh (Author); Artin Beytari (Corresponding author); Mohammadreza Ghorbanian, Hossein Badiei (Author)
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
