To value an option-free bond, we must determine the on-the-run yield curve for the particular issuer whose bond we have to value. This on-the-run yield curve used for valuation process is considered as the benchmark interest rates.
Let us consider the following on-the-run issue. The illustration deals with an option-free bond with four years remaining to maturity and a coupon rate of 6.5%.
Maturity
Yield to Maturity (%)
Market Price (in $)
1 year
3.4
100
2 years
3.9
3 years
4.7
4 years
5.0
Each bond is trading at par value i.e., at $100, so the coupon rate is equal to the yield to maturity.
Using the bootstrapping method, the spot rates are determined as follows:
Years
Spot Rates (%)
1
3.3000
2
3.9098
3
4.8120
4
5.0586
Using spot rates, we can calculate the present value of the cash flows.
= $105.374