Hostname: page-component-745bb68f8f-hvd4g Total loading time: 0 Render date: 2025-01-12T11:35:00.578Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  06 April 2009

Alan J. Marcus  and
David M. Modest
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 21 , Issue 1 , March 1986 , pp. 73 - 86
Copyright
Copyright © School of Business Administration, University of Washington 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Anderson, Ronald W. “The Determinants of the Volatility of Futures Prices.” Manuscript, New York: Columbia University (1981).Google Scholar
[2]Black, Fischer, and Scholes, Myron. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, Vol. 81 (05/06 1973), pp. 637–659.CrossRefGoogle Scholar
[3]Bodie, Zvi, and Rosansky, Victor I.. “Risk and Return in Commodity Futures.” Financial Analysts Journal, Vol. 36 (05/06 1980), pp. 3–14.CrossRefGoogle Scholar
[4]Breeden, Douglas T. “Consumption Risk in Futures Markets.” Journal of Finance, Vol. 35 (05 1980), pp. 503–520.CrossRefGoogle Scholar
[5]Brennan, Michael J., and Schwartz, Eduardo S.. “The Pricing of Equity-Linked Life Insurance Policies with an Asset Value Guarantee.” Journal of Financial Economics, Vol. 3 (06 1976), pp. 195–213.CrossRefGoogle Scholar
[6]Brennan, Michael, and Solanki, R.. “Optimal Portfolio Insurance.” Working Paper No. 666, British Columbia, Canada: University of British Columbia (1979).Google Scholar
[7]Congressional Budget Office. Agricultural Price Support Programs: A Layman's Guide. Washington D.C.: Government Printing Office (1976).Google Scholar
[8]Constantinides, George M. “Market Risk Adjustment in Project Valuation.” The Journal of Finance, Vol. 33 (05 1978), pp. 603–616.CrossRefGoogle Scholar
[9]Cox, John C., and Ross, Stephen A.. “The Valuation of Options for Alternative Stochastic Processes.” Journal of Financial Economics, Vol. 3 (01/03 1976), pp. 145–166.CrossRefGoogle Scholar
[10]Dusak, Katherine. “Futures Trading and Investor Returns: An Investigation of Commodity Market Risk Premiums.” Journal of Political Economy, Vol. 81 (10 1973), pp. 1387–1406.CrossRefGoogle Scholar
[11]Fischer, Stanley. “Call Option Pricing when the Exercise Price is Uncertain, and the Valuation of Index Bonds.” The Journal of Finance, Vol. 33 (03 1978), pp. 169–176.CrossRefGoogle Scholar
[12]George, P.S., and Kirby, G.A.Consumption Demand for Commodities in the United States with Projections for 1980. Berkeley, CA: Giannini Foundation Monograph no. 26, (03 1971).Google Scholar
[13]Leland, Hayne E. “Who Should Buy Portfolio Insurance.” Journal of Finance, Vol. 35 (05 1980), pp. 581–594.CrossRefGoogle Scholar
[14]Merton, Robert M. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Sciences, Vol. 4 (Spring 1973), pp. 141–183.CrossRefGoogle Scholar
[15]Merton, Robert M. “Option Pricing when Underlying Stock Returns Are Discontinuous.” Journal of Financial Economics, Vol. 5 (01/03 1976), pp. 125–144.CrossRefGoogle Scholar
[16]Merton, Robert M. “On the Pricing of Contingent Claims and the Modigliani-Miller Theorem.” Journal of Financial Economics, Vol. 5 (11 1977), pp. 241–249.CrossRefGoogle Scholar
[17]Samuelson, Paul A. “Proof that Properly Anticipated Prices Fluctuate Randomly.” Industrial Management Review, Vol. 6 (Spring 1965), pp. 41–49.Google Scholar
[18]Sosin, Howard B. “On the Valuation of Federal Loan Guarantees to Corporations.” Journal of Finance, Vol. 35 (12 1980), pp. 1209–1221.CrossRefGoogle Scholar
[19]Sundaresan, M. “The Valuation of Commodity Futures Prices.” Unpublished Ph.D. Dissertation, Pittsburgh, PA: Carnegie-Mellon University, (09 1980).Google Scholar
[20]U.S. Code: Congressional and Administrative News, No. 10 (02 1982).Google Scholar
[21]U.S. Office of Management and Budget. Special Analyses Budget of the United States Government Fiscal Year 1984, Special Analysis F (1984).Google Scholar
[22]Wall Street Journal (04 22, 1982), p. 47.CrossRefGoogle Scholar