Using GBM and GFBM to Forecast the Performance of the Bank Sector in Saudi Arabia.

Abstract

The future index prices are considered a central issue because investors and traders hope to know the future performance of the market. Numerous models have developed for this purpose. Geometric Brownian motion (GBM) is well-known model. This study investigates four types of GBM based on the existence of memory or the type of volatility. These models involve classical GBM, SV GBM, GFBM, and SV GFBM. These models were employed in an empirical study to forecast the future index prices of three banks in the Saudi Stock Exchange Market; Rajhi Bank, Riyadh Bank, and Ahli Bank. The evaluation was conducted using two criteria: mean square error (MSE) and mean absolute percentage error (MAPE). The results show that the smallest MSE and MAPE values were obtained for the SV GFBM for the three banks. These outcomes have confirmed the direct positive effect of taking memory and stochastic volatility assumptions into account in the GBM model, which was confirmed by some works. In general, all models considered in this work exhibited high accuracy with MAPE value of ≤ 10%. This finding supports the ability of these models to apply in a real financial environment. Through this study, we can conclude that the banking sector in Saudi Arabia is stable and predictable, and we encourage investors to trade in this sector.