Assume that annual interest rate volatility is 25% and current Treasury par bond yields for various maturities are as follows:

Maturity Par Rate

1 Year 1.28%

2 Years 1.87%

3 Years 2.04%

4 Years 2.07%

Construct a binomial interest rate tree, showing (1-year forward) rates at Years 0, 1, 2 and 3, that is consistent with the spot rates implied by the above par rates and the assumed interest rate volatility. Demonstrate that your tree correctly values a 6% annual coupon, $100 par value option-free bond with exactly 4 years to maturity.

The interest rate tree diagramed below pertains to the next four questions. You may assume that all of the bonds being valued in these questions are free of default risk.

The tree assumes 20% annual interest rate volatility and is constructed from the following Treasury spot rates:

Year 1: 0.50%

Year 2: 1.50%

Year 3: 2.40%

Year 4: 3.00%

2.52% 2.73% 2.02% 3.76% 4.08% 0.50% 5.60% 3.01% 6.08% 8.36% Year 0 Year 1 Year 2 Year 3 2.52% 2.73% 2.02% 3.76% 4.08% 0.50% 5.60% 3.01% 6.08% 8.36% Year 0 Year 1 Year 2 Year 3