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B. Estimate term structure of discount factors, spot rates and forward rates by

ID: 2788040 • Letter: B

Question

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 2.3 3.3 4.3 5.3 6.3 96.3 97.3 98.3 99.3 100.3

Explanation / Answer

Answer:- PARAMETER A,PARAMETER B,PARAMETER C

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