Journal of Resources and Ecology ›› 2020, Vol. 11 ›› Issue (1): 111-120.

### Option Pricing for Coffee Price Using Jump Diffusion Models

Tesfahun BERHANE*, Molalign ADAM, Guriju AWGICHEW, Eshetu HAILE

1. Department of mathematics, Bahir Dar University, Bahir Dar, P.O. Box 79, Ethiopia
• Received:2019-07-02 Accepted:2019-09-20 Online:2020-01-30 Published:2020-01-30
• Contact: Tesfahun Berhane, E-mail:tesfahunb2002@gmail.com

Abstract: In this study, we aim at developing a model for option pricing to reduce the risks associated with Ethiopian coffee price fluctuations. We used daily closed Washed Sidama class A Grade3 (WSDA3) coffee price recorded in the period 31 May 2011 to 30 March 2018 obtained from Ethiopia commodity exchange (ECX) market to analyse the price fluctuation. The nature of log-returns of the price is asymmetric (negatively skewed) and exhibits high kurtosis. We used jump diffusion models for modeling and option pricing the coffee price. The method of maximum likelihood is applied to estimate the parameters of the models. We used the root mean square error (RMSE) to test the validation of the models. The values of RMSE for Merton’s and double exponential jump diffusion models are 0.1093 and 0.0783, respectively. These results indicate that the models fit the data very well. We used analytical and Monte Carlo technique to find the call option pricing of WSDA3 price. Based on the empirical results, we concluded that double exponential jump diffusion model is more efficient than Merton’s model for modeling and option pricing of this coffee price.