Question

1. You observe the following set of spot rates: Time Period Oyly Oy2y Оузу Rate 2.25% 2.75% 3.10% You also estimate that future interest rate volatility is 10%, which leads to the following binomial interest rate tree: 4.647% 3.5930% 2.25% 3.8046 2.9417% 3.115% What is the value of a bond that matures in exactly 2 years, has par value of $100, an annual coupon of 4.4%, and is not callable? 2. What is the value of a bond identical that of Problem #1 but is callable in 1 year at a price of 101? 3. Relative to your answer in #2, what would happen to the price of the bond if it was callable at par? Explain in 1-2 sentences. 4. Relative to your answer in #2, what would happen if the future interest rate volatility was 5% rather than 10%? Explain in 1-2 sentences. 5. What would happen to the duration of the bond in Ex. 2 if interest rates decrease. Explain in 1-2 sentences.

Answer 1

1.) $ 103.18
2.) $ 102.97

Bond Matung in 2 year 8.59307 TOO + 4.4 2.85% 108.18 100+ 4.4 2.9417% T02 Today year I 1100.78+101.424.4 = 100-78 1 108.18 104.4 1.035930 1.0225 = 101.42 104-4 to24 1.029417 Callalile Bond @ 10.1 104.4 3.5930%. 100 78 2.25h | 102.97 104.4 2.9417% 1015 yedi I year 2 Today 107 100 78 to 102.97 1.0225

3.) If Bond is callable at Par then Value at Node 1 & 2 for Year 1 will be capped at $100 + $4.4. Thus value at Node 0 will be $102.10

4.) If Volatality is lowered to 5% instead of 10% then the value of a callable bond would increase. This happens due to the value of call option embedded in the bond is affected the value of straight bond remains unaffected. Thus is volatality is lowered call option woul gain thus increasing the calue of a callable bond.