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All Journal Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika
Christoffel Mario
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Mathematics

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Penerapan Model Geometric Brownian Motion Untuk Prediksi Saham dan Analisis Risiko Kerugian Sianturi, Tiurmaida; Christoffel Mario; Simamora, Tabita Paulina; Siahaan, Linda Natasya
Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika Vol. 8 No. 3 (2025): Volume 8 Nomor 3 Tahun 2025 (July - September)
Publisher : Universitas Cokroaminoto Palopo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30605/proximal.v8i3.5813

Abstract

This study aims to predict the stock price of Apple Inc. (AAPL) using the Geometric Brownian Motion (GBM) model and to analyze risk through a Monte Carlo Simulation-based Value at Risk (VaR) approach. Daily stock price data of Apple Inc. from January 1, 2022, to December 31, 2024, is used and split into training and testing datasets. The data analysis techniques involve calculating stock returns using the geometric return approach, testing normality with the Kolmogorov-Smirnov test, estimating GBM model parameters, simulating stock prices using Monte Carlo simulation in R software, evaluating prediction accuracy with Mean Absolute Percentage Error (MAPE), and assessing risk using Value at Risk (VaR) along with backtesting. The results show that the GBM model has good accuracy, with a Mean Absolute Percentage Error (MAPE) of 12.32%. The VaR risk analysis at 95% and 99% confidence levels shows no violations, indicating a conservative model. This study contributes to stock price prediction and investment risk management.
Co-Authors Siahaan, Linda Natasya Sianturi, Tiurmaida Simamora, Tabita Paulina