Given the following prices for an on-the-run bonds

1. Given the following prices for an on-the-run bonds: Bond Price 6-month Zero Coupon 98-18+ 1-year Zero Coupon 97-043 1.5-year with coupon rate of 3% 95-255 2-year with coupon rate of 4% 94-031 a. Construct the spot rate (bond-equivalent yield) for 6-month, 1-year, 1.5-year and 2-year using the bootstrapping methodology. (20 marks) b. Find the no-arbitrage price of the off-the-run 2-year bond with coupon rate of 2%, quoted with the same format as given in the question. Assume semiannual compounding and coupons are paid semiannually. (5 marks) 2. Given the following spot rates: Year Spot Rate (Annualized) 0.5 3.5% 1.0 4% 1.5 3.5% 2.0 5.5% c. Find the 6-month forward rates 6 months, 1 year, and 1.5 year from now respectively and express as annualized rates on a bond-equivalent basis. (15 marks) d. A 2-year bond is priced at 101 using the given spot rate curve. What is the coupon rate of the bond? Assume semiannual compounding and coupons are paid semiannually. (10 marks)