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Abstract
Stocks have high volatility, with price fluctuations that are difficult to predict and often do not meet the assumption of a normal distribution. The Brownian Motion method is widely used in stock price modeling, but is unable to capture sharp spikes in leptokurtic data. The Variance Gamma model is applied by evaluating a modified Brownian Motion process using a random time following a Gamma process. This model has three parameters to control volatility, kurtosis, and skewness. This research analyzes the daily stock return data of PT Industri Jamu dan Farmasi Sido Muncul from December 2023 to December 2024. TheVariance Gamma parameter estimation using the Moment Method and Maximum Likelihood Method. Accuracy calculation uses Mean Absolute Percentage Error (MAPE). The results showed that the Variance Gamma model with the normal standard process approach of a gamma process produced a MAPE of 4.150345%. While the different approach of two independent Gamma processes has a MAPE of 4.515595%. Both methods are more accurate when compared to the Geometric Brownian Motion with Jump model, which has a MAPE of 6.866523%. Variance Gamma has a smaller MAPE value, so it is more suitable for modeling stock prices with jumps and not normally distributed.
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References
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