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Pricing Commodity Options when the Underlying Futures Price Exhibits Time-Varying Volatility

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  • Robert J. Myers
  • Steven D. Hanson

Abstract

Standard commodity option pricing models assume proportional changes in the underlying futures price are i.i.d. normal. Empirical evidence suggests commodity futures price movements exhibit excess kurtosis and time-varying volatility. This paper presents option pricing models when time-varying volatility and excess kurtosis in the underlying futures price can be modeled as a GARCH process. Empirical results suggest that the GARCH option pricing model outperforms the standard Black option-pricing model, which uses historical volatilities. A closed-form approximation model using a variance forecast generated from the estimated GARCH process also outperforms Black's model and in many cases the general GARCH model as well.

Suggested Citation

  • Robert J. Myers & Steven D. Hanson, 1993. "Pricing Commodity Options when the Underlying Futures Price Exhibits Time-Varying Volatility," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 75(1), pages 121-130.
    • Handle: RePEc:oup:ajagec:v:75:y:1993:i:1:p:121-130.
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    Cited by:

    1. Karali, Berna & Ramirez, Octavio A., 2014. "Macro determinants of volatility and volatility spillover in energy markets," Energy Economics, Elsevier, vol. 46(C), pages 413-421.
    2. Wojciechowski, Jan & Ames, Glenn C.W. & Turner, Steven C. & Miller, Bill R., 2000. "Marketing Of Cotton Fiber In The Presence Of Yield And Price Risk," Journal of Agricultural and Applied Economics, Southern Agricultural Economics Association, vol. 32(3), pages 1-9, December.
    3. Du, Wen, 2004. "International Market Integration Under Wto: Evidence In The Price Behaviors Of Chinese And Us Wheat Futures," 2004 Annual meeting, August 1-4, Denver, CO 20115, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    4. Stentoft, Lars, 2005. "Pricing American options when the underlying asset follows GARCH processes," Journal of Empirical Finance, Elsevier, vol. 12(4), pages 576-611, September.
    5. Du, Wen & Wang, H. Holly, 2004. "Price behavior in China's wheat futures market," China Economic Review, Elsevier, vol. 15(2), pages 215-229.
    6. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    7. Michèle Breton & Javier de Frutos, 2010. "Option Pricing Under GARCH Processes Using PDE Methods," Operations Research, INFORMS, vol. 58(4-part-2), pages 1148-1157, August.
    8. Czudaj, Robert L., 2019. "Dynamics between trading volume, volatility and open interest in agricultural futures markets: A Bayesian time-varying coefficient approach," Econometrics and Statistics, Elsevier, vol. 12(C), pages 78-145.
    9. Nanying Wang & Jack E. Houston, 2016. "The Co-Movement between Non-GM and GM Soybean Prices in China: Evidence from Dalian Futures Market (2004-2014)," Applied Economics and Finance, Redfame publishing, vol. 3(4), pages 37-47, November.
    10. Wang, Nanying & Houston, Jack, 2015. "The Comovement between Non-GM and GM Soybean Price in China: Evidence from Dalian Futures Market," 2015 Annual Meeting, January 31-February 3, 2015, Atlanta, Georgia 196775, Southern Agricultural Economics Association.
    11. Koekebakker, Steen & Lien, Gudbrand D., 2002. "Term Structure of Volatility and Price Jumps in Agricultural Markets - Evidence from Option Data," 2002 International Congress, August 28-31, 2002, Zaragoza, Spain 24874, European Association of Agricultural Economists.
    12. N'zue Fofana & B. Wade Brorsen, 2001. "GARCH option pricing with implied volatility," Applied Economics Letters, Taylor & Francis Journals, vol. 8(5), pages 335-340.
    13. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    14. Wang, Nanying & Houston, Jack E., 2015. "The Co-movement between Non-GM and GM Soybean Price in China: Evidence from China Futures Market," 2015 Conference, August 9-14, 2015, Milan, Italy 211914, International Association of Agricultural Economists.
    15. Belleh Fontem & Megan Price, 2021. "Joint client selection and contract design for a risk-averse commodity broker in a two-echelon supply chain," Annals of Operations Research, Springer, vol. 307(1), pages 111-138, December.
    16. Hatem Ben-Ameur & Michèle Breton & Juan-Manuel Martinez, 2009. "Dynamic Programming Approach for Valuing Options in the GARCH Model," Management Science, INFORMS, vol. 55(2), pages 252-266, February.
    17. Hanson, Steven D. & Black, J. Roy & Wang, H. Holly, 2000. "Can Revenue Insurance Substitute For Price And Yield Risk Management Instruments?," Staff Paper Series 11655, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    18. Wang, Hong & Hanson, Steven D. & Myers, Robert J. & Black, Roy J., 1995. "Economic Implications of Alternative Crop Insurance Designs," Staff Paper Series 201206, Michigan State University, Department of Agricultural, Food, and Resource Economics.
    19. Thomas Url & Serguei Kaniovski, 2020. "The Potential Capital Requirement for a Minimum Prices Insurance Scheme for Wheat, Maize, and Rape Seed," WIFO Working Papers 601, WIFO.
    20. Tomek, William G. & Peterson, Hikaru Hanawa, 2000. "Risk Management In Agricultural Markets: A Survey," 2000 Producer Marketing and Risk Management Conference, January 13-14, Orlando, FL 19580, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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