In this paper we present a method for valuing American and European put and call options on debt securities. Although no exhange-traded options of this type currently exist in the United States, the Chicago Board Options Exchange plans to introduce option contracts on several government bonds, and the Chicago Board of Trade petitioned the Commodities Futures Trading Commission to allow the trading of options on the Ginny Mae futures contract. In addition to pricing put and call options, the model developed here can be applied to the valuation of other securities such as callable bonds and bank loan commitments.