B1 B2 B3 B4 B5 B6 B7 B8 B9 B10 5 6 7 8 9 99 100 101 102 103 B. Estimate term str
ID: 2788354 • Letter: B
Question
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
5
6
7
8
9
99
100
101
102
103
B. 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.Parameter a.
2.Parameter b.
3.Parameter c.
4.Current price of a dollar at 5th year.
5.Current price of a dollar at 7th year.
6.Current price of a dollar at 10th year.
7.Current price of a dollar at 15th year.
B1
B2
B3
B4
B5
B6
B7
B8
B9
B10
5
6
7
8
9
99
100
101
102
103
Explanation / Answer
1. Parameter a
2 Parameter b
3 Parameter c
Solution:
A1
A2
A4
A5
1
-217.2525
-243.4275
-269.6025
-295.7775
-321.953
2
-13363.07
-16777.06
-20579.01
-24768.91
-29346.8
3
-929126.8
-1307042
-1775630
-2344639
-3023821
C1
C2
C3
1
370278.8463
29309659.71
2665757566
2
29309659.71
2358268260
217698517593.55
3
2665757566
217698517593.55
20365322777504.20
A1
A2
A3
1
0.0117789674
-0.0003077150
0.0000017475
2
-0.0003077150
0.0000080709
-0.0000000460
3
0.0000017475
-0.0000000460
0.0000000003
C1
C2
C3
C4
C5
1
-0.070642113
0.011172536
0.053917579
0.040555
-0.04596
2
0.001739684
-0.000375748
-0.001451419
-0.001039
0.00131
3
-4.36856E-05
-4.57574E-05
-5.71849E-05
-8.09E-05
-0.00012
a
-0.105661333
b
0.001295726
c
-0.007777017
A1
A2
A4
A5
1
-217.2525
-243.4275
-269.6025
-295.7775
-321.953
2
-13363.07
-16777.06
-20579.01
-24768.91
-29346.8
3
-929126.8
-1307042
-1775630
-2344639
-3023821
C1
C2
C3
1
370278.8463
29309659.71
2665757566
2
29309659.71
2358268260
217698517593.55
3
2665757566
217698517593.55
20365322777504.20
A1
A2
A3
1
0.0117789674
-0.0003077150
0.0000017475
2
-0.0003077150
0.0000080709
-0.0000000460
3
0.0000017475
-0.0000000460
0.0000000003
C1
C2
C3
C4
C5
1
-0.070642113
0.011172536
0.053917579
0.040555
-0.04596
2
0.001739684
-0.000375748
-0.001451419
-0.001039
0.00131
3
-4.36856E-05
-4.57574E-05
-5.71849E-05
-8.09E-05
-0.00012
a
-0.105661333
b
0.001295726
c
-0.007777017
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