To value an option free bond, we can either use the sport rates or a binomial tree. Since both the methods are arbitrage free, the two values should be the same.
Consider an option-free bond with four years remaining to maturity, a coupon rate of 2%, and a par value of $100. Assume spot rates are as shown in Exhibit 3.
|Maturity (Years)||One-Year Spot Rate|
Then the bond value can be calculated as:
Next consider a binomial interest rate tree calibrated to the same spot curve (Exhibit 13).
We can then use the backward induction discounting process to obtain the bond value.
|Time 0||Time 1||Time 2||Time 3||Time 4|
The tree produces the same value for the bond as the spot rates and is therefore consistent with our standard valuation model.