A Simple Approach To Bond Option Pricing

Many authors have derived closed-form formulas for European options on discount bonds within a one-factor interest rate framework. The only known formula for European options on coupon-paying bonds is given by Jamshidian (1989), which is in the form of a portfolio of options on discount bonds. Not only does this approach require pricing of more than one options, it also requires that a threshold interest rate level be solved iteratively. When there are many coupons or when pricing is needed more frequently, Jamshidian's approach can be costly. In this paper, we show a very simple approach to pricing European options on bond portfolios. We not only do away with the requirement of calculating iteratively the threshold level of interest rate, but also reduce the calculation to only one option price. It also dramatically simplifies hedging. The key of this approach is to use a single discount bond to approximate the bond portfolio by matching durations.