Option Pricing for Coffee Price Using Jump Diffusion Models

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  • Department of mathematics, Bahir Dar University, Bahir Dar, P.O. Box 79, Ethiopia

Received date: 2019-07-02

  Accepted date: 2019-09-20

  Online published: 2020-01-30

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.

Cite this article

Tesfahun BERHANE, Molalign ADAM, Guriju AWGICHEW, Eshetu HAILE . Option Pricing for Coffee Price Using Jump Diffusion Models[J]. Journal of Resources and Ecology, 2020 , 11(1) : 111 -120 . DOI: 10.5814/j.issn.1674-764x.2020.01.011

References

1 Asfaw T F.2018. Evaluating the quality of coffee product on marketing performance of Ethiopian Commodity Exchange (ECX) Hawassa Branch.International Journal of Social Sciences Perspectives, 2(1): 50-79.
2 Askari H, Krichene N.2008. Oil price dynamics (2002-2006).Energy Economics, 30(5): 2134-2153.
3 Bakshi G, Cao C, Chen Z.1997. Empirical performance of alternative pricing models.Journal of Finance, 52: 2003-2049.
4 Ball C A, Torous W N.1985. On jumps in common stock prices and their impact on call option pricing.Journal of Finance, 40(1): 155-173.
5 Bart M, Seneshaw T, Tadesse K, et al.2014. Structural and Performance of Ethiopian’s Coffee Export Sector, International Food Policy Research Institutes (IFPRI): 1-34. https://ageconsearch.umn.edu/.
6 Birhan B, Daniel K, Tirufat D, et al.2013. Quality and value chain analysis of Ethiopian coffee.Journal of Agriculture and Social Research, 13(2): 35-41.
7 Charnes J M.2000. Using simulation for option pricing. In: Winter Simulation Conference. Orlando, USA: 151-157. https://pdfs.semanticscholar.org/.
8 Cont R, Tank P.2004. Financial modelling with jump processes, Chapman and Hall/CRC, UK.
9 DeFusco R A, McLeavey D W, Pinto J E, et al. 2001. Quantitative methods for investment analysis. Baltimore, USA: United Book Press.
10 Global Agricultural Information Network (GAIN). 2016. Coffee annual report: Assessment commodity and trade issue made by USDA staff. GAIN report No. ET-1615: 1-6.
11 Hanson F B, Westman J.2002. Stochastic analysis of jump diffusions for financial log-return processes. New York, USA: Springer-Verlag: 169-184.
12 Jia Q.2009. Pricing american options using Monte Carlo methods, U.U.D.M. Project Report, Department of Mathematics, Uppsala University. https://www.docin.com/p-1557054242.html.
13 Jondeau E, Poon S H, Rockinger M.2007. Financial modeling under Non-Gaussian distributions, London, UK: Springer.
14 Jorion P.1988. On jump processes in the foreign exchange and stock markets.Review of Financial Studies, 1(4): 427-445.
15 Kabeta T.2017. Review of coffee value chain in Ethiopia on the course crop value chain management,American Journal of Supply Chain Management, 2(1): 16-34.
16 Kou S G.2002. A jump diffusion model for option pricing.Management Science, 48(8): 1086-1101.
17 Kou S G, Wang H.2004. Option pricing under a double exponential jump diffusion model.Management Science, 50(9): 1178-1192.
18 Kou S G.2008. Jump-diffusion models for asset pricing in financial engineering, Handbooks in OR and and MS: Elsevier B V: 15.
19 Merton R C.1976. Option pricing when underlying stock returns are discontinuous.Journal of Financial Economics, 3: 125-144.
20 Tian X, Benkrid K, Gu X.2008. High performance Monte-Carlo based option pricing on FP- Gas.Engineering Letters, 16(3): 434-442.
21 Troster B.2015. Global commodity chains, financial markets, and local market structures: Price risks in the coffee sector in Ethiopia, Austrian Foundation for Development Research. Working Paper No. 56, Vienna, Austria: 1-31.
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