A Dissertation Submitted in Partial Fulfillment of the Requirements for the Degree of
Master’s in Mathematical and Computer Sciences and Engineering of the Nelson
Mandela African Institution of Science and Technology
The stock price is characterized by several features which can only be captured by the best
model. To investigate this the Merton's jump-diffusion model was developed and applied to
the selected stocks of three East African communit y countries’ stock markets. The daily
closing stock prices of the Nairobi Securities Exchange, the Dar es Salaam Stock Exchange
and Uganda Securities Exchange over a period of five (5) years from 1
st
July, 2013 to 1
st
July,
2018 were analyzed. The objective of this analysis was to investigate how best the developed
model do price options when the stock price features of three East African stock markets are
incorporated into the model. The Merton's jump-diffusion model was employed as a
stochastic differential equation. While the Maximum Likelihood Estimation method was used
to estimate the optimal model parameters and implemented with MATLAB. For comparison
purpose, the researcher estimated the parameters of the Black- Scholes model. The empirical
results show that the Merton Jump Diffusion gives realistic option price values for the
selected stocks due to the incorporation of the compound Poison process. On the other hand,
the selected stocks from all three markets exhibit several jumps as it was evidenced from
non-zero values of jump intensities (lambda). Also, the log-returns density of Merton reveals
the presence of volatility and leptokurtic features due to the presence of both negative and
positive skewness and excessive kurtosis values.
Keywords: Kurtosis, Options, Leptokurtic.