Hybrid Geometric Brownian Motion-Markov Switching untuk Peramalan Harga Saham Indonesia

Aldan Maulana Hamdani; Nur Iriawan; Irhamah Irhamah

doi:10.37905/euler.v13i3.35300

Hybrid Geometric Brownian Motion-Markov Switching untuk Peramalan Harga Saham Indonesia

Aldan Maulana Hamdani, Nur Iriawan, Irhamah Irhamah

Abstract

This study aims to analyse the performance of a stock price forecasting model based on Geometric Brownian Motion (GBM) modified with a Markov Switching (MS) approach. The research gap addressed is the limitation of the classical GBM model, which assumes constant volatility and is therefore unable to capture sudden changes in market regimes. To address these limitations, this study proposes a hybrid GBM-MS model as its main scientific contribution, in whichthe drift and volatility parameters are dynamically estimated following changes in market conditions through a switching mechanism between regimes. Parameter estimation is performed using the Hidden Markov Model. The model's performance is compared with the classical GBM as a benchmark. The research uses daily closing price data of PT Bank Central Asia Tbk. (BBCA) shares for the period 1 July – 30 December 2024. The results show that the hybrid GBM-MS model provides better forcasting accuracy with a MAPE value of 2.25% on training data and 1.38% on testing data, lower than the classical GBM model. These findings confirm that the integration of Markov Switching enhances the model's adaptability in capturing structural changes and market volatility. Practically, the hybrid GBM-MS model can be used as a more reliable forecasting and risk management tool to support investment decision-making, especially in dynamic and unstable market environments.

Keywords

GBM; Hybrid GBM-MS; Stock; Volatility

Full Text:

PDF

References

“PT Bursa Efek Indonesia,” Produk Saham. Accessed: Oct. 21, 2025. [Online]. Available: https://www.idx.co.id/

A. M. Hamdani, F. Widhiatmoko, and S. Fitri, “Perbandingan Akurasi Metode Autoregressive Integrated Moving Average dan Geometric Brownian Motion untuk Peramalan Harga Saham Indonesia,” Euler J. Ilm. Mat. Sains Dan Teknol., vol. 13, no. 1, pp. 14–20, Apr. 2025, doi: 10.37905/euler.v13i1.30760.

N. Hasan, F. A. O. Pelleng, and J. V. Mangindaan, “Analisis Capital Asset Pricing Model (CAPM) Sebagai Dasar Pengambilan Keputusan Berinvestasi Saham (Studi pada Indeks Bisnis-27 di Bursa Efek Indonesia),” J. Adm. BISNIS, vol. 8, no. 1, p. 36, Mar. 2019, doi: 10.35797/jab.8.1.2019.23498.36-43.

“Otoritas Jasa Keuangan.” Pasar Modal. Accessed: Oct. 21, 2025. [Online]. Available: https://ojk.go.id/id/Default.aspx

“Bank Central Asia.” Laporan Tahunan. Accessed: Nov. 12, 2025. [Online]. Available: https://www.bca.co.id/id/tentang-bca/Hubungan-Investor/laporan-presentasi/Laporan-Tahunan

S. Martha and S. W. Rizki, “Simulasi Pergerakan Harga Saham Menggunakan Pendekatan Metode Monte Carlo”. J. Untan. vol. 7, no. 2, p. 119-126.

D. M. Putri and L. H. Hasibuan, “Penerapan Gerak Brown Geometrik Pada Data Saham PT. ANTM,” MAp Math. Appl. J., vol. 2, no. 2, pp. 1–10, Dec. 2020, doi: 10.15548/map.v2i2.2258.

D. A. Maulana, A. Sofro, D. Ariyanto, R. W. Romadhonia, A. Oktaviarina, and M. D. Purna-ma, “Stock Price Prediction And Simulation Using Geometric Brownian Motion-Kalman Fil-ter: A Comparison Between Kalman Filter Algorithms,” BAREKENG J. Ilmu Mat. Dan Terap., vol. 19, no. 1, pp. 97–106, Jan. 2025, doi: 10.30598/barekengvol19iss1pp97-106.

C.-Y. Fang, Y. Liu, Z.-Y. Shi, and C. Chen, “Closed-Form Expression of Geometric Brownian Motion with Regime-Switching and Its Applications to European Option Pricing,” Symmetry, vol. 15, no. 3, p. 575, Feb. 2023, doi: 10.3390/sym15030575.

J. D. Hamilton, "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, vol. 57, no. 2, 1989.

F. Klaassen, “Improving GARCH Volatility Forecasts with Regime-Switching GARCH,” Em-pirical Economics, vol. 27, pp. 363-394, 2002.

W. Sulistyawati and S. Trinuryono, “Analisis (Deskriptif Kuantitatif) Motivasi Belajar Siswa Dengan Model Blended Learning Di Masa Pandemi Covid19,” Kadikma, vol. 13, no. 1, pp. 68-73, 2022.

M. Barua, T. Kumar, K. Raj, and A. M. Roy, “Comparative Analysis of Deep Learning Models for Stock Price Prediction in the Indian Market,” FinTech, vol. 3, no. 4, pp. 551–568, Nov. 2024, doi: 10.3390/fintech3040029.

D. Ruppert and D. S. Matteson, Statistics and Data Analysis for Financial Engineering: with R examples. in Springer Texts in Statistics. New York, NY: Springer New York, 2015. doi: 10.1007/978-1-4939-2614-5.

A. Sinha, “Daily and Weekly Geometric Brownian Motion Stock Index Forecasts,” J. Risk Fi-nanc. Manag., vol. 17, no. 10, p. 434, Sept. 2024, doi: 10.3390/jrfm17100434.

G. F. Dar, T. R. Padi, S. Rekha, and Q. F. Dar, “Stochastic Modeling for the Analysis and Forecasting of Stock Market Trend using Hidden Markov Model,” Asian J. Probab. Stat., pp. 43–56, June 2022, doi: 10.9734/ajpas/2022/v18i130436.

M. A. Maricar, “Analisa Perbandingan Nilai Akurasi Moving Average dan Exponential Smoothing untuk Sistem Peramalan Pendapatan pada Perusahaan XYZ,”, J. Sistem dan In-formatika, vol. 13, no. 2, pp. 36-45, 2019.

DOI: https://doi.org/10.37905/euler.v13i3.35300