Merton’s Jump Diffusion Model an Application to Stock Markets of East African Countries
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Date
2019-08-16Author
Novat, Kimaro
Charles, Wilson Mahera
Masanja, Verdiana Grace
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The 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.