Modelling stocks price in Ghana: application of geometric fractional brownian motion

Abstract

This study uses the Geometric Fractional Brownian Motion (GFBM) model to simulate stock price path and test whether the simulated stock prices mimic the actual stock returns. The model incorporates Hurst index which delimit the constant volatility assumptions and was estimated using the moment generating function. The sample for this study was based on the large Ghanaian companies listed on the Ghana Stock Exchange (GSE). Daily stock price data was obtained from the GSE database over the period January 2018 to December 2018. The results find increasing evidence that, the GFBM model consistently predict the stock price over all time horizon. There was a little above 80% chance that a stock price simulated using GFBM move in the same direction as the actual stock price. Finally, the average percentage error of the GFBM model was 16.68% or an accuracy of 83.32% while the GBM model generated an average percentage error of 20.90% or an accuracy of 79.10%. This indicates that, the GFBM model yielded better predicting accuracy than that of the GBM on almost all the selected stocks in the long-run and partly in the short-run.