Consider the following three bonds. Bond A is a 1-year zero-coupon bond. Bond B is a 3- year bond that pays 150 in coupons every year and its current price in the market is =

1,362.80. Bond C is a 3-year bond that pays 100 in coupons every year and its current price

in the market is = 1,222.64. All three bonds make a principal payment of 1,000 upon their

expiration. Finally, the one-year spot rate is equal to = 3%.

a)Using the no-arbitrage condition, find the fair price for bond A.

b)Use the above information to estimate and plot the 3-year yield curve.

c)Suppose that the yield curve that you calculated in part b changes so that the 3-year yield-to-maturity increases by one percentage point, but the 1-year and 2-year yields-to- maturity remain the same. Calculate the modified duration and the modified convexity

for the three bonds.