Note: please assume annual compounding of interest for these problems.
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
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.
4. What is the value of the embedded call option?
5. Suppose the market price of the 3-year callable bond is 100.125, what is the option adjusted spread?