Q3

You are given the following information about the current yields to maturity (YTM) of three riskless, coupon-paying bonds:

Maturity (years) Coupon rate (annual payments) YTM (EAR)

1 2

3.00% 6.00% 2.000% 3.457%

3

5.00% 6.745%

Note that these are yields on coupon-paying bonds and that the coupon payments are annual, with the first coupon payment occurring exactly one year from today. Assume that there is no arbitrage.

a) b) c)

Determine the yield to maturity of a two-year zero-coupon bond. (8 points) Determine the yield to maturity of a three-year zero-coupon bond.

Yet another subprime mortgage crisis has just struck, and the part of the yield curve corresponding to years 1 and 2 computed in parts (a) and (b) has just shifted downwards by 2%. The part of the yield curve corresponding to years 3 and beyond remained the same. Determine the price of a three-year coupon- paying bond with annual coupon payments and a coupon rate of 8.00%.