Application of Binomial Tree in Determining the Price of an Asian Option and Calculation of Risk-Sensitive Parameters (Case Study: Soybean Meal and Corn)

Document Type : Research Article

Authors

• E. Pishbahar
• M. Baghestani
• Gh. Dashti

University of Tabriz

https://doi.org/10.22067/jead2.v32i1.62744

Abstract

Introduction: The use of new financial instruments, and specifically option contracts, as a tool for risk management and create profitability, can help to boom exchanges and reduce the problems of the agricultural sector. Given the increasing population and the growing need for animal protein, the fluctuation in prices of these products can have a significant impact on the food security of individuals. The fluctuation of the prices of production inputs, including soybean meal and corn, can lead to fluctuations in the price of meat. The Iran Mercantile Exchange can play a major role in eliminating concerns and concerns of market participants for strategic agricultural products, including soybean meal and corn, using derivatives such as futures contracts and options. The trend of development of commodity exchanges in the world suggests that the emergence and development of these markets activities in the field of economy, seeks to dispel some of the economic needs and in many cases, eliminate some of the bottlenecks and barriers in the commodity market. The trend of development of commodity exchanges in the world suggests that the emergence and development of these markets activities in the field of economy, seeks to dispel some of the economic needs and in many cases, eliminate some of the bottlenecks and barriers in the commodity market. Option contracts is one of derivatives in commodity exchange that can have effective roll in agricultural market for overcome the problems of traditional market and reduce the risk of investors in this market. According to population, growth and increasing demand for Chicken meat and eggs, soybean meal and maize prices volatility may be fluctuating prices for white meat and egg. According to this, the aim of this study is determine the price of Asian option and Sensitivity parameters.
Materials and Methods: Among quantitative methods to calculate derivatives and risk sensitivity parameters of an option, binomial tree model is frequently used. Arithmetic and Geometric Asian option with fixed and floating expiration prices were calculated using the binomial tree model for soybean meal and maize. Moreover, the sensitivity of an option's price to changes (Change in the price of the underlying asset, Delta, price volatility, time until maturity and risk-free interest rate) measured by using sensitive parameters and the impact has been obtained. Required information includes historical data on the weekly prices of soybean meal and corn in the years 2007-16.
Results and Discussion: The results indicate that an Asian option is cheaper than a European simple option. Increase in asset prices, increase in asset price volatility and increases risk-free interest rate, increase the price of call option. By reducing the remaining time to maturity (T), with other factors constant, the value of an option is reduced. The hedge ratio for soybean meal is equal to 0.69 and 0.81 for corn, which means that in order to reduce the income fluctuations due to changes in the price of soybean and corn, 69 and 81 percent of the products must be sold in future and option markets. Two methods of Monte Carlo simulation and binomial tree model were used to determine the price of Asian option whit fixed strike for soybean meal and corn were 12.5 and 9.2, respectively. The results indicate that the control variate in variance reduction Monte-Carlo simulation method has a very good performance and significantly reduced the variance. Increase in asset prices, increase in asset price volatility and increases risk-free interest rate, increase the price of call option.
Conclusions: In general, it can be said that to adopt a proper position in an option, is necessary to consider all the variables affecting the price. In addition, according to the sensitivity of an option to each of these variables, it should consider a good strategy to hedge these contracts. The option is a good tool for risk management, but it is also associated with risks. In volatile markets where volatility is high, the value of options is changing rapidly. Therefore, risk managers should regularly review the value of an option and thoughtful strategies to update these changes, because perhaps once-profitable option other time is extremely unprofitable.

Keywords

• Binomial model
• Greeks
• Mercantile exchange
• Option
• Premium

20.1001.1.20084722.1397.32.1.1.0

References

1. Abdolahi M., and Najafi B. 2003. Study the Possibility of using futures and options markets in reduce price volatility in agricultural products in Iran: Case Study pistachios. Agricultural economy and Development, 11 (41-42): 1-25. (In Persian)

2. Box G.E.P., and Jenkins G.M. 1976. Time series analysis: forecasting and control, Revised edition, Holden-day, San Francisco, 45-56.

3. Boyle Ph., and Potapchik A. 2008. Price and sensitivities of Asian options: A survey. Insurance: Mathematics and Economics, 42, 189-211.

4. Carr P., and Madan D. 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance, 2(40), 61-73.

5. Chung S.F., and Wong H.Y. 2014. Analytical pricing of discrete arithmetic Asian options with mean reversion and jump. Journal of Banking & Finance, Accepted Manuscript.

6. Cox J. C., Ross S. A., and Rubinstein M. 1979. Option pricing: A simplified approach. Journal of Financial Economics, 7 (3): 229.

7. Derakhshan M. 2011. Derivatives and Risk Management in markets of Oil. Institute for International Energy Studies.

8. Fusai G., Marena M., and Roncorono A. 2008. Analytical pricing of discretely monitored Asian-style options: Theory and application to commodity markets. Journal of Banking & Finance, 32, 2033-2045.

9. Horvath A., and Medvegyev P. 2016. Pricing Asian Options: A Comparison of numerical and simulation approaches twenty years later. Journal of Mathematical Finance, 6, 810-841.

10. Hosseini S., and Abedi S. 2007. Assessment the role of market components and government policies in determining the price of corn in Iran. Jornal of Agricultural Economics, 1: 21-33. (In Persian)

11. Hull J.C. 2009. Fundamentals of futures and options markets. 7th Edition.

12. Hull J., and White A. 1993. Efficient procedures for valuing European and American path-dependent options. Journal of derivatives, 1, 21-31.

13. Jaakko R., Samu K., Markus K., and Tuomas R. 2014. The pricing of Asian commodity options. Aalto University School of Science, Seminar on Case Studies in Operations Research, Mat-2.4177.

14. Kimiagari A.M., and Afarideh Sani E. 2006. Suggestion a composed option pricing model based on Black-Scholes and Binomial tree models (case study in Tehran stock exchenge). International Journal of Industrial Engineering & Production Research, 19(4): 119-127. (In Persian with English abstract)

15. Mombeini, H., Hashempour, M., and Rowshandel, SH. 2015. Proposing a novel model based on ARIMA technique for forecasting housing price: a case study of Tehran. Iranian Journal of Investment Knowledge, 14(4): 15-28.

16. Moon, K.S., Jeong, Y., and Kim, H. 2016. An efficient binomial method for pricing Asian options. Economic Computation and Economic Cybernetics Studies and Research, 2(50), 151-164.

17. Nabavi chashmi A., and Gahsemi Chali J. 2014. Binomial tree used in the calculation of risk-sensitive parameters and options on stock price. Journal of Management, 11(34): 101-119. (in Persian)

18. Soleimani Sarvestani Kh., and Ebrahimi K. 2012. Binomial Tree Method for Asian options in Jump-diffusion Models. 3rd Conference on Financial Mathematics & Applications. Semnan University.

19. Yahyazadeh M., and Hasannejad M. 2006. Feasibility of the utilization option in Iran capital market. Message Management, (17&18): 85-107.

20. Zhanh H. 2009. Pricing Asian options using Monte Carlo methods. Project Report, Uppsala University.