GEOMETRIC BROWNIAN MOTION WITH JUMP DIFFUSION AND VALUE AT RISK ANALYSIS OF PT BANK NEGARA INDONESIA STOCKS

Abstract

Investments in stocks are made to make a profit, where the higher the expected profit, the greater the risk undertaken. The return on investing in stocks can be influenced by changes in the price of stocks that are difficult to predict, which can lead to uncertainty in the value of the return and the risk of the stock. The application of the Geometric Brownian Motion (GBM) model with Jump Diffusion is crucial for enhancing the accuracy of stock price forecasting and risk analysis by incorporating price jumps resulting from external events within complex market dynamics. The data used in this study are the closing price data of the daily stock of PT Bank Negara Indonesia for the period 1 December 2022 to 31 January 2024, where the stock return data has a kurtosis value greater than 3 (leptokurtic) so that the data indicates a jump. The GBM with Jump Diffusion model was implemented to predict the stock price with a simulation repetition of 1000 times. The analysis shows that the GBM model with Jump Diffusion has an excellent accuracy rate with the smallest MAPE value of 0.86%. The average value of the VaR with Monte Carlo simulation obtained at the reliability levels of 80%, 90%, 95%, and 99% in a row is 0.96%, 1.53, 1.97%, and 2.64%. This result shows that the higher the confidence level used, the greater the risk.