PENERAPAN MODEL GEOMETRIC BROWNIAN MOTION DAN PERHITUNGAN NILAI VALUE AT RISK PADA SAHAM BANK CENTRAL ASIA TBK - Fadhilah Rizky Aulia; Evy Sulistianingsih; Wirda Andani (EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN, 2023)
Stock price fluctuations are difficult to predict, resulting in uncertain profits. Therefore, a mathematical model is needed to predict future stock prices, namely the Geometric Brownian Motion (GBM) model based on a stochastic process. Stocks are also accompanied by risks that have potential for loss. The risk can be measured using Value at Risk (VaR) which can estimate the maximum loss that may happen from an investment at a certain level of confidence and period of time. The purpose of this research is to implement the GBM model in predicting stock prices and estimating the maximum loss of stock investment using VaR. This research analyzes the daily closing stock price of PT Bank Central Asia (BBCA) for the period November 1, 2021, to December 31, 2022. The stock price predictions with the GBM model are used to estimate the VaR value. Based on the analysis results, GBM is highly accurate model with an average MAPE value of 5.77% and the smallest MAPE value of 1.45%. The VaR values obtained at the 80%, 90%, 95% and 99% confidence level are 1,17%, 1,74%, 2,19% and 2,86% of the total fund investment for the next one-day period, respectively.