Application of the Geometric Brownian Motion Model and Value at Risk Calculation on the Stock of PT Bank Tabungan Negara (Persero) Tbk: Stock of PT Bank Tabungan Negara (Persero) Tbk

Natasya Pradini Putri; Angela Ratna Sari Palbeno

doi:10.47194/ijgor.v6i4.407

Authors

Natasya Pradini Putri
Angela Ratna Sari Palbeno
angela22005@mail.unpad.ac.id

Keywords:

Geometric Brownian Motion, Value at Risk, Monte Carlo, stock

Abstract

The fluctuating nature of stock prices creates risks for investors, making quantitative methods essential for predicting price movements and estimating potential losses. This study applies the Geometric Brownian Motion (GBM) model to simulate the stock price dynamics of PT Bank Tabungan Negara (Persero) Tbk (BBTN) and calculates the Value at Risk (VaR) using the Monte Carlo simulation method. Daily closing price data from May 26 to September 26, 2025, were analyzed and confirmed to follow a normal distribution based on the Kolmogorov–Smirnov test. The results indicate a high prediction accuracy with a Mean Absolute Percentage Error (MAPE) of 7.95%. The estimated daily VaR for an initial capital of IDR 100,000,000 ranges from IDR 97,974 to IDR 114,045, corresponding to confidence levels between 80% and 99%. Keywords: Geometric Brownian Motion, Value at Risk, Monte Carlo, stock.

References

Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.

Bodie, Z., Kane, A., & Marcus, A. J. (2014). Investments (10th ed.). McGraw-Hill Education.

Fabozzi, F. J., Focardi, S. M., & Kolm, P. N. (2010). Quantitative Equity Investing: Techniques and Strategies. John Wiley & Sons.

Glasserman, P. (2004). Monte Carlo Methods in Financial Engineering. Springer-Verlag.

Gujarati, D. N., & Porter, D. C. (2009). Basic Econometrics (5th ed.). McGraw-Hill.

Hersugondo, H., Ghozali, I., Handriani, E., Trimono, T., & Pamungkas, I. D. (2022). Price Index Modeling and Risk Prediction of Sharia Stocks in Indonesia. Economies, 10(1), 1–13.

Hull, J. C. (2018). Options, Futures, and Other Derivatives (10th ed.). Pearson.

Jorion, P. (2007). Value at Risk: The New Benchmark for Managing Financial Risk (3rd ed.). McGraw-Hill.

Lewis, C. D. (1982). Industrial and Business Forecasting Methods. Butterworth Scientific.

Maruddani, D. A. I., Trimono, T., & Mas'ad, M. (2022). Implementation of Stochastic Model for Risk Assessment on Indonesian Stock Exchange. Media Statistika, 15(2), 151–162.

Mensah, E. T., et al. (2023). Simulating stock prices using geometric Brownian motion: modified approaches and applications. International Journal of Financial Modeling.

Morkūnaitė, I. (2024). Evaluation of Value-at-Risk (VaR) using the Gaussian Mixture Model and comparisons with Monte Carlo GBM methods. Vilnius University ePublications.

Muslimin, M. (2021). Comparison of Stock Price Risk Measurement of BUMN Banking Stocks: Empirical Evidence on BRI and BNI. BIJAK – Bulletin of Indonesian Banking and Finance.

Øksendal, B. (2013). Stochastic Differential Equations: An Introduction with Applications (6th ed.). Springer.

Ross, S. M. (2014). Introduction to Probability Models (11th ed.). Academic Press.

Samuelson, P. A. (1965). Rational Theory of Warrant Pricing. Industrial Management Review, 6(2), 13-39.

Sinha, A., et al. (2024). Daily and Weekly Geometric Brownian Motion Stock Index Forecasts and Reliability Tests. Journal of Risk and Financial Management, 17(10), 434. https://doi.org/10.3390/jrfm17100434

Tandelilin, E. (2010). Portofolio dan Investasi: Teori dan Aplikasi (Edisi Pertama). Kanisius.

Taylor, H. M., & Karlin, S. (1998). An Introduction to Stochastic Modeling (3rd ed.). Academic Press.

Widyarti, E. T., Maruddani, D. A. I., Trimono, T., & Hersugondo, H. (2021). Blue Chip Stocks Valuation and Risk Prediction on The Indonesia Stock. Academy of Accounting and Financial Studies Journal, 25(6), 1–14.