Estimate term structure of discount factors, spot rates and forward rates by using data on five semi-annual coupon paying bonds with $100 face value each. The bonds, respectively, have 1.25, 5.35, 10.4, 15.15, and 20.2 years to maturity; pay coupon at annual rates of 10.59, 11.59, 12.59, 13.59 and 14.59 percent of face value; and are trading at quoted spot market prices in dollars of 104.59, 105.59, 106.59, 107.59, and 108.59. Specify the discount factor function d(t) by a third degree polynomial with unknown parameters a, b, and c. Using estimated d(t) function, determine spot rate and forward rate functions by assuming half-year compounding. Then write the values of the following based on your estimation.
1. Coefficient of parameters a, b and c in first bond price equation
2. Coefficient of parameters a, b and c in second bond price equation
3. Coefficient of parameters a, b and c in third bond price equation
4. Coefficient of parameters a, b and c in fourth bond price equation
5. Coefficient of parameters a, b and c in fifth bond price equation
6. Parameters a, b and c
7. Current price of a dollar at 5th, 7th, 10th and 15th year
8. Spot rate for terms 2, 5, 10, and 17 year
9. Forward rate for half year periods:
2.5 - 3.0 years
5.5 - 6.0 years
10.5 - 11.0 years
15.5 - 16.0 years