Option Pricing on Commodity Prices Using Jump Diffusion Models

Subject Areas : International Journal of Mathematical Modelling & Computations

Tesfahun Berhane ¹ , Molalign Adam ² , Eshetu Haile ³

1 - Bahir Dar University, Department of Mathematics, Bahir Dar, Ethiopia.
2 - Bahir Dar University, Department of Mathematics, Bahir Dar, Ethiopia
3 - Bahir Dar University, Department of Mathematics, Bahir Dar, Ethiopia

Received: 2019-01-05 Accepted : 2019-03-11 Published : 2019-01-01

Keywords: Skewness, Kurtosis, Option pricing, Jump diffusion model, Risk neutral measure, Commodity prices,

Abstract :

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.