a) The 1-year, 2-year and 3-year (continuously compounded) zero rates are 2%, 3.5% and

4.5%, respectively.

i) Calculate the prices of a 1-year zero coupon bond, a 2-year zero coupon bond and a

3-year coupon-bearing bond that pays a coupon of 2 at the end of each year.

ii) Assume that a 4-year coupon-bearing bond that pays a coupon of 4 at the end of each year sells for 94.607. Calculate the continuously compounded 4-year zero rate.

For all bonds, assume a face value of 100

b) For the 3-year and 4-year coupon-bearing bonds from part (a), calculate the annually

compounded yield to maturity and duration. If there is a 70bps (annually compounded)

increase in the annually compounded yields, calculate the duration predicted percentage

change of the bonds' prices.

c) Consider the zero rate curve of part (a). Calculate the three implied forward rates and the value of a forward rate agreement (FRA) that offers a rate of 9% (semiannually

compounded) for one year, starting in three years. Design a strategy that takes advantage

of possible arbitrage opportunities and calculate the present value of the profit. For the FRA value and the arbitrage strategy calculations, assume a principal of 100 million.

d) Your assistant has found a 5-year bond, which pays a coupon of 5 at the end of each year and currently sells for 103. Assuming that all interest rates are non-negative and no

arbitrage opportunities exist in the bond market, can your assistant be correct? What is the maximum 5-year bond price implied by the assumptions mentioned above? For your

calculations, use the zero rates curve from part (a).

e) Discuss briefly the main reasons why hedging may lead to an increase in the firm value.

When can hedging lead to a worse situation?