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 - Putri, Natasya Pradini; Palbeno, Angela Ratna Sari (iora, 2025)
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.