The Valuation of a Random Number of Put Options: An Application to Agricultural Price Supports
用金融理论中的或有债权方法，为美国农业价格支持等政府保险项目中的随机数量看跌期权推导估值公式，并估算出某些作物价值因此提升高达9%。
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 op? tions 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 for? mula. 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.