A comparative analysis of stochastic models for stock price forecasting: The influence of historical data duration and volatility regimes

Mulualem Kahssay; Shihan Miah; Mulualem Kahssay; Shihan Miah

doi:10.3934/QFE.2025021

Quantitative Finance and Economics

2025, Volume 9, Issue 3: 602-630. doi: 10.3934/QFE.2025021

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Research article

A comparative analysis of stochastic models for stock price forecasting: The influence of historical data duration and volatility regimes

Mulualem Kahssay ,
Shihan Miah ^,

School of Computing and Engineering, University of West London, St Marys Road, London W5 5RF, UK

Received: 03 February 2025 Revised: 15 June 2025 Accepted: 29 July 2025 Published: 04 August 2025
JEL Codes: C53

Accurate stock price forecasting is essential for informed financial decision-making. This study presents a comparative analysis of four foundational stochastic models—Geometric Brownian Motion (GBM), the Heston Stochastic Volatility model, the Merton Jump-Diffusion (MJD) model, and the Stochastic Volatility with Jumps (SVJ) model—each formulated to capture distinct features of financial market dynamics. Utilizing maximum likelihood estimation (MLE) for parameter calibration and Monte Carlo simulation for forecasting, we assessed model performance over varying historical calibration windows (3-month, 6-month, and 1-year) and a 3-months prediction horizon. Empirical findings demonstrate that the SVJ model consistently achieves superior predictive performance, as quantified by root mean square error (RMSE) and mean absolute percentage error (MAPE), across assets with both low and high volatility profiles. Moreover, the analysis reveals that for low-volatility stocks, such as AAPL and MSFT, a 1-year calibration window yields lower forecast errors, whereas for high-volatility stocks, such as TSLA and MRNA, a 6-month calibration window provides improved forecasting accuracy. These results highlight the importance of selecting model structures and estimation periods that align with the underlying volatility characteristics of the asset.
- Geometric Brownian Motion,
- Heston Stochastic Volatility,
- Merton Jump-Diffusion,
- Stochastic Volatility with Jumps,
- stock price forecasting,
- Monte Carlo Simulation
Citation: Mulualem Kahssay, Shihan Miah. A comparative analysis of stochastic models for stock price forecasting: The influence of historical data duration and volatility regimes[J]. Quantitative Finance and Economics, 2025, 9(3): 602-630. doi: 10.3934/QFE.2025021

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Abstract

Accurate stock price forecasting is essential for informed financial decision-making. This study presents a comparative analysis of four foundational stochastic models—Geometric Brownian Motion (GBM), the Heston Stochastic Volatility model, the Merton Jump-Diffusion (MJD) model, and the Stochastic Volatility with Jumps (SVJ) model—each formulated to capture distinct features of financial market dynamics. Utilizing maximum likelihood estimation (MLE) for parameter calibration and Monte Carlo simulation for forecasting, we assessed model performance over varying historical calibration windows (3-month, 6-month, and 1-year) and a 3-months prediction horizon. Empirical findings demonstrate that the SVJ model consistently achieves superior predictive performance, as quantified by root mean square error (RMSE) and mean absolute percentage error (MAPE), across assets with both low and high volatility profiles. Moreover, the analysis reveals that for low-volatility stocks, such as AAPL and MSFT, a 1-year calibration window yields lower forecast errors, whereas for high-volatility stocks, such as TSLA and MRNA, a 6-month calibration window provides improved forecasting accuracy. These results highlight the importance of selecting model structures and estimation periods that align with the underlying volatility characteristics of the asset.

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