<![CDATA[Fluctuations in stock prices and its random nature make stocks volatile and difficult for financial managers and investors to predict future stock prices. The path of stock can be described in relation to the random collision of tiny particles suspended in the molecules of liquid. In examining the martingale property in stock prices, this article examined whether stock price log follows a normal distribution and whether the expected mean and the expected volatility in stock is an increasing function of time. The sample for this study was based on listed monthly stock data quoted on the Nigerian stock exchange for a period of five years (2015-2019). The test of normality was conducted using the Kolmogorov-Smirnov test statistic and the geometric Brownian motion model was employed as the method of data analysis. Results of the analysis showed that the log of stock price follows a normal distribution, it also showed that the expected mean and expected volatility of stock price is an increasing function of time, depicting randomness and fluctuations in its path as a result of the market shocks and volatility.]]>
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