Stochastic Forecasting of Stock Prices in Nigeria: Application of Geometric Brownian Motion Model

Purpose:  The purpose of the study is to model and simulate the trends and behavioral patterns in The Nigerian Stock Market and hence predict the future stock prices within the Geometric Brownian Motion (GBM) framework. Methodology: The methodology involves a comparison of forecasted daily closing prices to actual prices in order to evaluate the accuracy of the prediction model. Based on the model assumptions of the GBM with drift: continuity, normality and Markov tendency, the study investigated four years (2015 - 2018) of historical closing prices of ten stocks listed on The Nigerian Stock Exchange. The sample for this study is based on the most continuously traded stocks. Findings: The results show that in the simulation there are some actual stock prices located outside trajectory realization that may be from GBM model. Thus, the model did not predict accurately the price behavior of some of the listed stocks.  The predictive power of the model is declining towards the longer the evaluated time frame proven by the higher value of the mean absolute percentage error. The value of the MAPE is 50% and below for the one- to two-year holding periods, and above 50% for the three-year holding period. Unique Contribution to theory, Practice and Policy:  The MAPE and directional prediction accuracy method provide support that over short periods the GBM model is accurate. Meaning that the GBM is a reasonable predictive model for one or two years, but for three years, therefore, it is an inaccurate predictor. It is recommended that the technical analyst whose primary motive is to make gain at the expense of other participants should identify high volatile portfolio in any holding period for effective prediction Investors with long-range holding position as investment strategy should concentrate more on low capitalized stocks rather than stocks with large market capitalization. This is a unique contribution to theory, practice and policy.