In this paper, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian commodity prices fluctuations. We used the daily closed Unwashed Lekempti grade 5 (ULK5) coffee and Whitish Wollega Sesame Seed Grade3 (WWSS3) prices obtained fro More
In this paper, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian commodity prices fluctuations. We used the daily closed Unwashed Lekempti grade 5 (ULK5) coffee and Whitish Wollega Sesame Seed Grade3 (WWSS3) prices obtained from Ethiopia commodity exchange (ECX) market to analyse the prices fluctuations.The natures of log-returns of the prices exhibit asymmetric heavy tails and high kurtosis. We used jump diffusion models for modeling and option pricing on commodity prices. The method of maximum likelihood is applied to estimate the parameters under the models. The root mean square error (RMSE) is used to test the goodness of fitting for the models to thedata. This test indicates that the models fit the data well. The techniques of analytical and Monte Carlo simulation are used to find the call option pricing of the commodity prices. Based on the empirical results, we conclude that double exponential jump diffusion model is more efficient than Merton’s model for modeling and option pricing of the commodity prices.
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In this study we model the daily rainfall occurrence using Markov Chain Analogue Yearmodel (MCAYM) and the intensity or amount of daily rainfall using three different probability distributions; gamma, exponential and mixed exponential distributions. Combining the occurr More
In this study we model the daily rainfall occurrence using Markov Chain Analogue Yearmodel (MCAYM) and the intensity or amount of daily rainfall using three different probability distributions; gamma, exponential and mixed exponential distributions. Combining the occurrence and intensity model we obtain Markov Chain Analogue Year gamma model (MCAYGM), Markov Chain Analogue Year exponential model (MCAYEM) and Markov Chain Analogue Year mixed exponential model (MCAYMEM). The models are assessed using twenty nine-years(1987-2015) of historical records of daily rainfall data taken from three different locations which are obtained from Ethiopian National Meteorology Agency (ENMA). Both maximum likelihood and least square techniques are used in the estimation of model parameter. The results indicate that all the three model are suitable for the simulation of precipitation process. In order to assess their performance we apply both qualitative (graphical demonstration) and quantitative techniques. In the quantitative, the performance of the three models; MCAYEM, MCAYGM and MCAYMEM are measured using mean absolute error(MAE) and have mean absolute error of 0.45mm, 0.57 mm and 0.42mm respectively for kiremet(June to September) rainfall which is the long rainy season in Ethiopia. These accuracy is mainly because of the new component that is Analogue Year (AY) used in the modeling of frequency of daily rainfall included in the Markov chain (MC) process. Based on these model we obtain an option price for Teff crop for different months. The result shows an excellent accuracy with only maximum absolute error of 0.54 currency.
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