8/18/2019 Yield Curve Interpolation

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8/18/2019 Yield Curve Interpolation

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3 4 5 6 7 8 9 10

ar Interpolation

Spot Yield

Forward YieldVertices

 Years

8/18/2019 Yield Curve Interpolation

3/9

 Yield Curve Interpolation

Oserved #itted $is"ount &n '$t( Spot $is"ount #orard

 Years !erti"es Curve #a"tor '$t( Yield #a"tor Yield

0   4.0000% 4.0000% 1.0000 0.0000   4.0000% 1.0000 4.0000%

1   5.0000%   0.9524   )0.0488   5.0000% 0.9518 5.0625%2   5.0000%   5.0000%   0.9070 )0.0976   4.9984% 0.9060 5.0593%

3   5.9976%   0.8397 -0.1747 6.0556% 0.8361 8.3540%

4   6.5000%   6.5000%   0.7773 )0.2519   6.5952% 0.7714 8.3914%

5   6.5833%   0.7270 -0.3188 6.6668% 0.7204 7.0741%

6   6.6388%   0.6800 -0.3857 6.7132% 0.6729 7.0661%

7   6.6785%   0.6360 -0.4525 6.7453% 0.6285 7.0585%

8   6.7083%   0.5949 -0.5194 6.7685% 0.5871 7.0512%

9   6.7315%   0.5564 -0.5863 6.7858% 0.5485 7.0441%

10   6.7500%   6.7500%   0.5204 )0.6532   6.7990% 0.5124 7.0372%

1

      Y      i    e      l      d

8/18/2019 Yield Curve Interpolation

4/9

0 1 2 3 4 5 6 7 8 9 10

.0000%

.0000%

.0000%

.0000%

.0000%

.0000%

.0000%

.0000%

.0000%

.0000%

&o* &inear 

Spot Cr!e

Forw ard Cr!e

Vertices

 Years

8/18/2019 Yield Curve Interpolation

5/9

 Yield Curve Interpolation

Oserved #itted Spot $is"ount #orard

 Years !erti"es Curve Yield #a"tor Yield

0   4.0000% 4.0000%   4.0000% 1.0000 4.0000%

1   4.3922% 4.3922% 0.9579 4.3922%

2   5.0000% 5.0000%   5.0153% 0.9068 5.6421%

3   5.7328% 5.7880% 0.8447 7.3506%

4   6.5000% 6.5000%   6.6277% 0.7736 9.1869%

5   7.2109% 7.4409% 0.6985 10.7560%

6   7.7750% 8.1137% 0.6262 11.5415%

7   8.1016% 8.5048% 0.5648 10.8816%

8   8.1000% 8.4521% 0.5225 8.0839%

9   7.6797% 7.8096% 0.5083 2.8048%

10   6.7500% 6.7500%   6.5169% 0.5319 -4.4422%

0 1 2 3

-6.0000%

-4.0000%

-2.0000%

0.0000%

2.0000%

4.0000%

6.0000%

8.0000%

10.0000%

12.0000%

14.0000%

      Y      i    e      l      d

8/18/2019 Yield Curve Interpolation

6/9

&a*ran*e er-s

4.0000% 0.0000% 0.0000% 0.0000%

1.3500% 4.2188% -1.2188% 0.0422%

0.0000% 5.0000% 0.0000% 0.0000%

-0.3500% 3.2813% 2.8438% -0.0422%

0.0000% 0.0000% 6.5000% 0.0000%

0.7500% -3.9063% 10.1563% 0.2109%

1.6000% -7.5000% 13.0000% 0.6750%

2.2500% -9.8438% 14.2188% 1.4766%

2.4000% -10.0000% 13.0000% 2.7000%

1.7500% -7.0313% 8.5313% 4.4297%

0.0000% 0.0000% 0.0000% 6.7500%

/0 Y

0  /

1 Y

1  /

2 Y

2  /

3 Y

3

4 5 6 7 8 9 10

+ol,no-ial #it

Spot Cr!e

Forw ard Cr!e

Vertices

 Years

8/18/2019 Yield Curve Interpolation

7/9

 Yield Curve Interpolation

Oserved #itted Spot $is"ount #orard

 Years !erti"es Curve Yield #a"tor Yield

0 4.0000% 4.0000%   4.0000% 1.0000 4.0000%

1   4.4345% 4.4345% 0.9575 4.4345%2 5.0000% 5.0000%   5.0142% 0.9068 5.5972%

3   5.7591% 5.8153% 0.8440 7.4357%

4 6.5000% 6.5000%   6.6255% 0.7737 9.0937%

5   6.9975% 7.1842% 0.7069 9.4483%

6   7.2464% 7.4604% 0.6494 8.8518%

7   7.2964% 7.4942% 0.6030 7.6972%

8   7.1971% 7.3373% 0.5675 6.2457%

9   6.9984% 7.0517% 0.5416 4.7938%

10 6.7500% 6.7500%   6.7051% 0.5226 3.6359%

0 1 2 3

0.0000%

1.0000%

2.0000%

3.0000%

4.0000%

5.0000%

6.0000%

7.0000%

8.0000%

9.0000%

10.0000%

 

      Y      i    e      l      d

8/18/2019 Yield Curve Interpolation

8/9

0 0 0 1   0

8 4 2 1   0

0 0 0 0   80 0 0 0   64

0 0 0 0 0

T =   0 0 0 0 0

12 4 1   0   )12

0 0 0 0   48

12 2   0 0   )12

0 0 0 0   24

0 2   0 0 0

0 0 0 0 0

Coefsa_0   0.0002184 0.032 -0.032 -0.036 0.036 0.001b_0   0.0000000 0.000 0.000 0.000 0.000 0.000c_0   0.0041263 -0.629 0.629 0.145 -0.145 -0.005d_0   0.0400000 1.000 0.000 0.000 0.000 0.000a_1   -0.0004671 -0.036 0.036 0.056 -0.056 -0.007

b_1   0.0041129   =   0.411 -0.411 -0.556 0.556 0.048c_1   -0.0040995 -1.452 1.452 1.258 -1.258 -0.102d_1   0.0454839 1.548 -1.548 0.258 0.742 0.065a_2   0.0000829 0.001 -0.001 -0.007 0.007 0.002b_2   -0.0024866 -0.040 0.040 0.202 -0.202 -0.054

c_2   0.0222984 0.355 -0.355 -1.774 1.774 0.306

d_2   0.0102867 -0.860 0.860 4.301 -4.301 0.520

4 5 6 7 8 9 10

ui" Spline

Spot Cr!e

Forw ard Cr!e

Vertices

 Years

8/18/2019 Yield Curve Interpolation

9/9

0 0 0 0 0 0 0

0 0 0 0 0 0 0

4 2 1   0 0 0 016 4 1   0 0 0 0

0 0 0   64 16 4 1

0 0 0   1000 100 10 1

)4 )1   0 0 0 0 0

8 1   0   )48 )8 )1   0

)2   0 0 0 0 0 0

2   0 0   )24 )2   0 0

0 0 0 0 0 0 0

0 0 0   60 2   0 0

T Y -0.001 0.065 -0.008 0.040 -0.016 -0.105 0.008 0.04000.000 0.000 0.000 0.000 0.000 0.500 0.000 0.0500

0.005 -0.258 0.032 -0.161 0.065 -0.581 -0.032 0.0500

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.0650

0.007 -0.073 0.040 0.048 0.081 0.024 -0.040 0.0650

-0.048 0.823 -0.290 -0.548 -0.581 -0.274 0.290   X   0.06750.102 -2.903 0.613 1.935 1.226 0.968 -0.613 0.0000

-0.065 3.097 -0.387 -2.065 -0.774 -1.032 0.387 0.0000

-0.002 0.003 -0.011 -0.002 0.006 -0.001 0.039 0.0000

0.054 -0.081 0.323 0.054 -0.188 0.027 -0.656 0.0000

-0.306 0.710 -2.839 -0.473 1.656 -0.237 3.172 0.0000

0.480 -1.720 6.882 1.147 -4.014 0.573 -4.659 0.0000

-1