Forecasting the Performance of the Energy Sector at the Saudi Stock Exchange Market by Using GBM and GFBM Models

Future index prices are viewed as a critical issue for any trader and investor. In the literature, various models have been developed for forecasting index prices. For example, the geometric Brownian motion (GBM) model is one of the most popular tools. This work examined four types of GBM models in terms of the presence of memory and the kind of volatility estimations. These models include the classical GBM model with memoryless and constant volatility assumptions, the SVGBM model with memoryless and stochastic volatility assumptions, the GFBM model with memory and constant volatility assumptions, and the SVGFBM model with memory and stochastic volatility assumptions. In this study, these models were utilized in an empirical study to forecast the future index price of the energy sector in the Saudi Stock Exchange Market. The assessment was led by utilizing two error standards, the mean square error (MSE) and mean absolute percentage error (MAPE). The results show that the SVGFBM model demonstrates the highest accuracy, resulting in the lowest MSE and MAPE, while the GBM model was the least accurate of all the models under study. These results affirm the benefits of combining memory and stochastic volatility assumptions into the GBM model, which is also supported by the findings of numerous earlier studies. Furthermore, the findings of this study show that GFBM models are more accurate than GBM models, regardless of the type of volatility. Furthermore, under the same type of memory, the models with a stochastic volatility assumption are more accurate than the corresponding models with a constant volatility assumption. In general, all models considered in this work showed a high accuracy, with MAPE ≤ 10%. This indicates that these models can be applied in real financial environments. Based on the results of this empirical study, the future of the energy sector in Saudi Arabia is forecast to be predictable and stable, and we urge financial investors and stockholders to trade and invest in this sector.