Comparison of GBM, GFBM and MJD Models in Malaysian Rubber Prices Forecasting

Abstract

This research studies three mathematical models, namely geometric Brownian motion (GBM), geometric fractional Brownian motion (GFBM) model which was developed by adding the Hurst parameter to GBM to characterize the long-memory phenomenon, and Merton jump-diffusion (MJD) model which captures shocks via GBM. This study sets out to forecast Malaysia rubber prices for the six months period beginning in January 2022 and ending in June 2022, which involves four main steps; calculating the logarithmic return of rubber prices; estimating the parameters for forecasting the rubber prices using the three models; simulating the rubber prices using the GBM, GFBM and MJD models via Monte Carlo simulation; and computing the mean absolute percentage errors (MAPE) and forecast accuracy. Simulation results show that the MJD model is the most accurate model in forecasting the rubber prices.