Browsing by Author "Novat, Kimaro"

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Merton’s Jump Diffusion Model an Application to Stock Markets of East African Countries
(International Journal of Advances in Scientific Research and Engineering (ijasre), 2019-08-16) Novat, Kimaro; Charles, Wilson Mahera; Masanja, Verdiana Grace
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.
Option pricing using jump diffusion model: a case of stock markets of selected east African countries
(NM-AIST, 2020-03) Novat, Kimaro
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.