Geometric mean-reverting approach to modelling stock prices at the Uganda securities exchange:case of Stanbic bank Uganda

Abstract

An accurate stock price prediction brings advantages to investors and benefits the stakeholders directly since it provides enough information to make better investment decisions towards the future. This dissertation aims at predicting the stock prices of Stanbic Bank Uganda (SBU) at the Uganda Securities Exchange (USE) using the geometric mean-reverting (GMR) model.

In order to achieve this, the GMR model was solved using the 1-dimensional Itô’s lemma and its analytic solution was obtained. Its expected value and variance were obtained and used to discretize the analytic solution. The logarithm of the stock prices was normally distributed and the maximum log-likelihood estimation was used to obtain the parameters of the GMR model using the logarithms of the prices. This was done using a given set of historical data of SBU at USE.

The estimated parameters were then used to predict the stock prices of SBU at USE using another set of data from the historical prices. Two time periods were predicted that is, before and during the outbreak of COVID-19. Matlab R2017a, Excel and R software were utilized for simulations. The forecasting accuracy of the GMR model was evaluated by the mean absolute percentage error (MAPE). A 95% prediction interval in each time period (which included the actual future value with probability 95%) was also computed.

In order to compare the forecasting accuracy of the GMR model with time series models for stock price prediction, the stock prices of SBU were predicted using a mixed ARMA-GARCH model. The results obtained showed that the GMR model was more accurate than the mixed ARMA-GARCH model for predicting stock prices of SBU.