The on-the-run US Treasury par curve is as follows:
Maturity Coupon/YTM Market Price
1 3.50% $100
2 3.75% $100
3 4.00% $100
Using the bootstrapping methodology, the spot rates are:
Maturity Spot Rate
1 3.5000%
2 3.7547%
3 4.0134%
Assume 10% annual interest rate volatility
1. Calculate the binomial interest rate tree using the 2-year on-the-run issue and the 3-year on-the-run issue.
2. Validate the interest rate tree by valuing a 3-year 4.5% coupon option-free bond
a. price the bond using the spot rate curve
b. price the bond using the interest rate tree
3. Assume that the 3-year 4.5% bond is callable in Year 1 at (101) and in Year 2 at par. The call rule is to call whenever the price exceeds the call price. Calculate the value of the bond with the embedded option.