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 B1, B2, B3, B4, and B5 percent of face value; and are trading at quoted spot market prices in dollars of B6, B7, B8, B9 and B10. Specify the discount factor function d(t) by a third degree polynomial with unknown parameters a, b, and c, as done in class. 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. Current price of a dollar at 5th year.
2. Current price of a dollar at 7th year.
3. Current price of a dollar at 10th year.
4. Current price of a dollar at 15th year.
5. Spot rate for term 2 year.
6. Spot rate for term 5 year.
7. Spot rate for term 10 year.
8. Spot rate for term 17 year.
9. Forward rate for half year period 2.5 to 3.0 years.
10. Forward rate for half year period 5.5 to 6.0 years.
11. Forward rate for half year period 10.5 to 11.0 years.
12. Forward rate for half year period 15.5 to 16.0 years.
B1: 9.8
B2: 10.8
B3: 11.8
B4: 12.8
B5: 13.8
B6: 103.8
B7: 104.8
B8: 105.8
B9: 106.8
B10: 107.8