Question: Maturity 6m 1yr 2yr 3yr 5yr 7yr 10yr YTM (%) 0.07 0.11 0.37 0.76 1.61 2.24 2.78 Any required rates for other maturities should be computed using the linear interpolation method. (E.g. 9yr YTM = 2.24% + (2.78% - 2.24%) × 2/3 = 2.60%).
(1) Calculate the 6 monthly discount factors D(t) and the semi-annual zero coupon rates z(t), where t = 0.5, 1, 1.5, ., 9.5, 10. (2) Using the discount factors derived in (1), calculate the price of a 4½ year semi-annual coupon bond with an annual coupon rate of 4% and the face value 100. (3) Given the bond price derived in (2), estimate, using a try-and-error method or otherwise, the YTM of this 4½ year coupon bond. Why is this bond's YTM different to the market 4½ year rate estimated above?