Many prediction models have been developed and improved to assist investors in making investment decision by providing an overlook of the price paths, hence minimum investment risk. The geometric fractional Brownian motion (gfBm) model improves the accuracy of the price modelling by incorporating the Hurst exponent into the price dynamics, which provides information on the self-similarity level in each time series, therefore able to explain more behaviours of price changes.

The price St follows a geometric Brownian motion (gBm) when it follows the dynamics

where  is a Brownian motion, and the solution is

The gfBm is more general than the gBm, where the price follows the dynamics

where  is an fBm with

and the solution is

Both processes have constant drift μ and constant volatility σ.

This study applies the gBm and gfBm models to simulate price paths of Malaysian crude palm oil, and tests both models for accuracy of the simulations by comparing with the actual
prices, using the mean absolute percentage error (MAPE) taken relative to the simulated prices. For instance, for a 5-year period simulation, the MAPE using GBM is 10.9386, while the MAPE using
GFBM is 7.6137. This shows higher accuracy in the simulation by the GFBM model.

Assoc. Prof. Dr. Siti Nur Iqmal Ibrahim   Jabatan Matematik dan Statistik Fakulti Sains, Universiti Putra Malaysia Kepakaran: Matematik Kewangan Email: iqmal@upm.edu.my

Date of Input: 30/07/2024 | Updated: 30/07/2024 | norlida_mn