Stochastic Modeling Of Stock Prices On The Ghana Stock Exchange

Abstract

Financial models today rely on assumptions that make them insufficient in many real cases. The Geometric Brownian Motion model is assumed as a process for stock prices frequently. The study examined whether the behavior of weekly and monthly returns series of some selected equities listed on the Ghana Stock Exchange can be modeled with the Geometric Brownian Motion(GBM). The Augmented Dickey Fuller, Shapiro-Wilk, Ljung-box and some graphical methods are some statistical methods used to unveil the behavior of the returns. The study showed that only the monthly returns of Ghana Commercial Bank and Benso Oil Palm Plantation satisfied all the three assumptions of the Geometric Brownian Motion, however the Hurst exponent estimates showed that seven return series can be modeled by the Geometric Brownian Motion. To test the model, parameters were estimated for five equities and three subsequent months forecasts is made for which the accuracy of the estimation is measured by the error between the estimates and the actual price observed. The study showed that, the expected price of the equities modeled is close to the actual stock price realized on the Exchange even though some deviated slightly, however the entire actual prices observed lies within the estimated confidence interval. The study concluded that the monthly returns of the Ghana Stock Exchange is a better data set to be used for statistical inference as compared to the weekly returns and even though most of the returns exhibit long range dependency the Geometric Brownian Motion can be used for some equities on the Ghana Stock Exchange .