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. 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.

2. What is the value of the embedded call option?

3. Suppose the market price of the 3-year callable bond is 100.125, what is the option adjusted spread?