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

Alan Marcus and David M. Modest

Journal of Financial and Quantitative Analysis, 1986, vol. 21, issue 1, 73-86

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.

Date: 1986
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