The Pricing of Options on Default-Free Bonds

Recent developments in the finance literature dealing with the valuation of contingent claims have been triggered by Black and Scholes [2] with their valuation of European options on corporate stocks. The type of valuation model derived by Black and Scholes is attractive because it is independent of preferences. This independence is possible due to the fact that the contingent claims are usually assumed to be contingent on traded assets or traded state variables. For example, a European call option is a claim contingent on the value of the corresponding stock. To maintain the independence of the claim from preferences, however, some variables have to be discarded and considered as constants. For example, the rate of interest, which is not a traded state variable, is considered a constant in most of the literature (see Black and Scholes [2], Merton [11], and Ingersoll [9]). Though this approximation might not cause important discrepancies in the case of corporate liabilities and options on corporate liabilities, the effect of such an approximation on the value of default-free bonds and options on default-free bonds is more important since these liabilities depend only on the rate of interest.