Take the bond price data given below on 50 bonds. Each bond has a face value of $100 and pays the given coupon semi-annually starting at the next coupon payment dates as given. Follow the steps discussed in class to estimate the term structures of discount factors, spot interest rates, and forward interest rates. Coupon is the rate in per cent per year applied to the face value of a bond to determine the annual coupon in dollars, half of which is paid every six months on coupon payment dates. For example, Coupon of 10% for a bond with a face value of $100 will result in $10 in annual coupon and a payment of $5 on each coupon payment date every half year.
Answer the following questions:
1-50: In the simplified bond price equation the coefficients of parameter “a” for the 50 bonds.
51-100: In the simplified bond price equation the coefficients of parameter “b” for the 50 bonds.
101-150: In the simplified bond price equation the coefficients of parameter “c” for the 50 bonds.
151-200: In the simplified bond price equation the left side number for the 50 bonds.
201: Estimated value of “a.”
202: Estimated value of “b.”
203: Estimated value of “c.”
To plot, take 100 values of the term (x-axis) at intervals of .25 year starting at time 0. Then produce the 100 values (y-axis) of discount factor function, forward rate and spot rate functions for the plots. Answer the following:
204-303: Discount factor function values for the 100 different terms .25, .50,….,25.00.
304-403: Forward rate function values for the 100 different terms .25, .50,….,25.00.
404-503: Spot rate function values for the 100 different terms .25, .50,….,25.00.
Bond QSP NextCoup Coupon YearsMat
1 117.42 0.372 23.60 0.872
2 117.99 0.384 24.20 1.384
3 118.56 0.396 24.80 1.896
4 119.13 0.408 25.40 2.408
5 119.70 0.420 26.00 2.920
6 120.27 0.432 26.60 3.432
7 120.84 0.444 27.20 3.944
8 121.41 0.450 27.80 4.450
9 121.98 0.450 28.40 4.950
10 122.55 0.450 29.00 5.450
11 123.12 0.450 29.60 5.950
12 123.69 0.450 30.20 6.450
13 124.26 0.450 30.80 6.950
14 124.83 0.450 31.40 7.450
15 125.40 0.450 32.00 7.950
16 125.97 0.450 32.60 8.450
17 126.54 0.450 33.20 8.950
18 127.11 0.450 33.80 9.450
19 127.68 0.450 34.40 9.950
20 128.25 0.450 35.00 10.450
21 128.82 0.450 35.60 10.950
22 129.39 0.450 36.20 11.450
23 129.96 0.450 36.80 11.950
24 130.53 0.450 37.40 12.450
25 131.10 0.450 38.00 12.950
26 131.67 0.450 38.60 13.450
27 132.24 0.450 39.20 13.950
28 132.81 0.450 39.80 14.450
29 133.38 0.450 40.40 14.950
30 133.95 0.450 41.00 15.450
31 134.52 0.450 41.60 15.950
32 135.09 0.450 42.20 16.450
33 135.66 0.450 42.80 16.950
34 136.23 0.450 43.40 17.450
35 136.80 0.450 44.00 17.950
36 137.37 0.450 44.60 18.450
37 137.94 0.450 45.20 18.950
38 138.51 0.450 45.80 19.450
39 139.08 0.450 46.40 19.950
40 139.65 0.450 47.00 20.450
41 140.22 0.450 47.60 20.950
42 140.79 0.450 48.20 21.450
43 141.36 0.450 48.80 21.950
44 141.93 0.450 49.40 22.450
45 142.50 0.450 50.00 22.950
46 143.07 0.450 50.60 23.450
47 143.64 0.450 51.20 23.950
48 144.21 0.450 51.80 24.450
49 144.78 0.450 52.40 24.950
50 145.35 0.450 53.00 25.450