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The Valuation of a Random Number of Put Options: An Application to Agricultural Price Supports

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  • Marcus, Alan J.
  • Modest, David M.

Abstract

We show that the U.S. agricultural price support system, and certain other government insurance programs, can be interpreted as the provision of a random number of put options to program beneficiaries. Because the number of puts being supplied is random, the value of the guarantees is no longer given by the standard Black-Scholes put option formula. This paper uses the contingent-claims methodology of modern finance theory to derive an appropriate valuation formula for such programs. We estimate the value to farmers of agricultural price supports for several commodities covered by the U.S. agricultural price support system. Our results indicate that the current system raises the ex ante value of some crops by as much as 9 percent. The method of valuation is applicable to other forms of government guarantees, as well, such as exchange rate insurance and export subsidy guarantees.

Suggested Citation

  • Marcus, Alan J. & Modest, David M., 1986. "The Valuation of a Random Number of Put Options: An Application to Agricultural Price Supports," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(1), pages 73-86, March.
    • Handle: RePEc:cup:jfinqa:v:21:y:1986:i:01:p:73-86_01
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    Citations

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    Cited by:

    1. Peter Bardsley & Paul Cashin, 1990. "Underwriting Assistance To The Australian Wheat Industry — An Application Of Option Pricing Theory," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 34(3), pages 212-222, December.
    2. Calum G. Turvey, 2010. "Biography," Agricultural Finance Review, Emerald Group Publishing Limited, vol. 70(1), pages 5-20, May.
    3. Knut K. Aase, 2004. "A Pricing Model for Quantity Contracts," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 71(4), pages 617-642, December.
    4. Calum G. Turvey & Jeffrey R. Stokes, 2008. "Market Structure and the Value of Agricultural Contingent Claims," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 56(1), pages 79-94, March.
    5. Richards, Timothy J. & Rickard, Bradley J., 2013. "Patents as Options: Path-Dependency and Patent Value," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149725, Agricultural and Applied Economics Association.
    6. Turvey, Calum G. & Toole, Andrew A. & Kropp, Jaclyn D., 2007. "An Empirical Examination of the Relationship Between Real Options Values and the Rate of Investment," 2007 1st Forum, February 15-17, 2007, Innsbruck, Austria 6606, International European Forum on System Dynamics and Innovation in Food Networks.
    7. Hall, Joyce A. & Brorsen, B. Wade, 1989. "The Policy Implications of Corn and Soybean·Supply Response to Risk," 1989 Annual Meeting, July 30-August 2, Baton Rouge, Louisiana 270502, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    8. Fackler, Paul L., 1989. "A Note On Alterntive Market And Governmental Risk Transference Mechanisms," Southern Journal of Agricultural Economics, Southern Agricultural Economics Association, vol. 21(2), pages 1-7, December.
    9. Richards, Timothy J. & Manfredo, Mark R., 2003. "Infrequent Shocks and Rating Revenue Insurance: A Contingent Claims Approach," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 28(2), pages 1-19, August.
    10. Menapace, Luisa & Turvey, Calum G., 2002. "An Empirical Examination of the Relationship Between Real Options Values and the Rate of Investment in the Food and Life Science Industries," 2002 Regional Committee NC-221, October 7-8, 2002, Denver, Colorado 132373, Regional Research Committee NC-1014: Agricultural and Rural Finance Markets in Transition.
    11. 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.
    12. Stinson, Thomas F. & Coggins, Jay S. & Ramezani, Cyrus A., 1998. "Was Fair Fair To U.S. Corn Growers? An Analysis Of The Payments Offered To Corn Growers Under The 1996 Federal Agricultural Improvement And Reform Act," 1998 Annual meeting, August 2-5, Salt Lake City, UT 20984, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    13. Turvey, Calum G. & Brorsen, B. Wade & Baker, Timothy G., 1988. "A Contingent Claim Pricing Model for Valuing Non-Recourse Loan Programs and Target Prices," 1988 Annual Meeting, August 1-3, Knoxville, Tennessee 270319, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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