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  4. Performance of geometric Brownian motion (GBM) with various volatility measurement models in forecasting market indices

Performance of geometric Brownian motion (GBM) with various volatility measurement models in forecasting market indices

MMC.
2025;
Volume 12, Number 1
: pp. 221–232
https://doi.org/10.23939/mmc2025.01.221
Received: November 19, 2024
Revised: February 17, 2025
Accepted: February 20, 2025

Shah N. A., Ariffin N. A. N.  Performance of geometric Brownian motion (GBM) with various volatility measurement models in forecasting market indices.  Mathematical Modeling and Computing. Vol. 12, No. 1, pp. 221–232 (2025)  

Authors:
  1. N. A. Shah
  2. N. A. N. Ariffin
1
College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM)
2
College of Computing, Informatics and Mathematics, Universiti Teknologi MARA (UiTM), Pahang Branch

Many investors use market indices to manage their portfolios and keep track of the financial markets.  Forecasting financial trends in a complex market is a critical factor for investors.  Given how challenging and unpredictable future predictions can be, forecasting market indices cannot rely solely on regular patterns based on technical analysis.  Therefore, this paper proposes a way to forecast future market indices of Financial Times Stock Exchange (FTSE) Bursa Malaysia Kuala Lumpur Stock Exchange Composite Index (KLCI) and MSCI All Country World Index (ACWI) by using geometric Brownian motion (GBM).  Four different types of formulae are used to determine the suitable volatility measurement that may yield forecast values closer to the actual movements of stock market indices.  The objective of this paper is to analyze the performance of geometric Brownian motion (GBM) and Simple Exponential Smoothing (SES) based on FBM KLCI and MSCI ACWI stock returns.  Mean Squared Error (MSE), Mean Absolute Percentage Error (MAPE) and Mean Absolute Deviation (MAD) are chosen to be used in this paper to measure accuracy.  The findings show that using high-low-close volatility yields forecast values closer to the actual movements of stock market indices.  Since SES has the smallest error values, it can be considered the most effective method for forecasting.

forecast market index
geometric Brownian motion
volatility
simple exponential smoothing
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