This research article published by the International Journal of Advances in Scientific Research and Engineering (ijasre), Volume 5, Issue 8 August - 2019The stock price is characterized with a number of features which can only be captured by a best model. To investigate this the Merton’s jump diffusion model was applied to the selected stocks of three East African community countries’ stock markets. The daily closing stock prices of the Nairobi Securities Exchange (NSE), the Dar es Salaam Stock Exchange (DSE) and Uganda Securities Exchange (USE) over a period of 5 years from 01/07/2013 to 01/07/2018 were analyzed with the objective of investigating how best the model captures the stock price features at these three East African stock markets. The Merton’s jump diffusion model was considered as a stochastic differential equation and the Maximum Likelihood Estimation (MLE) method was used to estimate the optimal model parameters and implemented with MATLAB. The empirical results show that, the selected stocks from all the three markets exhibit a number of jumps as it was evidenced from non-zero values of jump intensities (lambda). Also, the log returns density of Merton reveals presence volatility and leptokurtosis features as evidenced by the presence of both negative and positive skewness and excessive kurtosis values.