Figures and Tables
Feb 25, 2016
Figures and Tables
Fig 1aDEPOSIT_USD_3M
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
22-Sep-93 04-Feb-95 18-Jun-96 31-Oc t- 97 15-Mar-99 27-Jul- 00 09-Dec-01
Fig 1bDEPOSIT_USD_6M
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
22-Sep-93 04-Feb-95 18-Jun-96 31-Oc t- 97 15-Mar-99 27-Jul- 00 09-Dec-01
Fig 1cDEPOSIT_USD_1Y
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
22-Sep-93 04-Feb-95 18-Jun-96 31-Oc t- 97 15-Mar-99 27-Jul- 00 09-Dec-01
Fig 1dBOND_USD_2Y
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
22-Sep-93 04-Feb-95 18-Jun-96 31-Oc t- 97 15-Mar-99 27-Jul- 00 09-Dec-01
Fig 1eBOND_USD_5Y
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
22-Sep-93 04-Feb-95 18-Jun-96 31-Oc t- 97 15-Mar-99 27-Jul- 00 09-Dec-01
Fig 1fBOND_USD_10Y
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
22-Sep-93 04-Feb-95 18-Jun-96 31-Oc t- 97 15-Mar-99 27-Jul- 00 09-Dec-01
Fig 1gBOND_USD_20Y
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
22-Sep-93 04-Feb-95 18-Jun-96 31-Oc t- 97 15-Mar-99 27-Jul- 00 09-Dec-01
Fig 1hBOND_USD_30Y
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
22-Sep-93 04-Feb-95 18-Jun-96 31-Oc t- 97 15-Mar-99 27-Jul- 00 09-Dec-01
Fig 2aSerial Variance: DEPOSIT_USD_3M
0.0000
0.0020
0.0040
0.0060
0.0080
0.0100
0.0120
1 6 11 16 21 26 31 36 41 46 51 56 61 66
n-day non-overlapping changes
Fig 2bSerial Variance: DEPOSIT_USD_6M
0.000
0.002
0.004
0.006
0.008
0.010
0.012
1 6 11 16 21 26 31 36 41 46 51 56 61 66
n-day non-overlapping changes
Fig 2cSerial Variance: DEPOSIT_USD_1Y
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
1 6 11 16 21 26 31 36 41 46 51 56 61 66
n-day non-overlapping changes
Fig 2dSerial Variance: BOND_USD_2Y
0.000
0.002
0.004
0.006
0.008
0.010
0.012
0.014
0.016
1 6 11 16 21 26 31 36 41 46 51 56 61 66
n-day non-overlapping changes
Fig 2eSerial Variance: BOND_USD_10Y
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
1 6 11 16 21 26 31 36 41 46 51 56 61 66
n-day non-overlapping changes
Fig 2fSerial Variance: BOND_USD_20Y
0.000
0.001
0.002
0.003
0.004
0.005
0.006
0.007
1 6 11 16 21 26 31 36 41 46 51 56 61 66
n-day non-overlapping changes
Fig 2gSerial Variance: BOND_USD_30Y
0.000
0.001
0.002
0.003
0.004
0.005
0.006
1 6 11 16 21 26 31 36 41 46 51 56 61 66
n-day non-overlapping changes
Fig 3aDensity of curvatures: DEPOSIT_USD_3M to DEPOSIT_USD_1Y
0.00
0.02
0.04
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06
Fig 3bDensity of curvatures: DEPOSIT_USD_6M to BOND_USD_2Y
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
-0.01 0.00 0.01 0.02 0.03 0.04 0.05 0.06
Fig 3cDensity of curvatures: BOND_USD_5Y to BOND_USD_20Y
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
-0.0
002
-0.0
001
0.00
00
0.00
01
0.00
02
0.00
03
0.00
04
0.00
05
0.00
06
0.00
07
0.00
08
Fig 3dDensity of curvatures: BOND_USD_10Y to BOND_USD_30Y
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
-0.0
0003
5
-0.0
0003
0
-0.0
0002
5
-0.0
0002
0
-0.0
0001
5
-0.0
0001
0
-0.0
0000
5
0.00
0000
0.00
0005
0.00
0010
0.00
0015
Fig 4
0
0.002
0.004
0.006
0.008
0.01
0.012
0 2 4 6 8 10 12 14 16 18 20
Fig 5
Lag-1 Serial Autocorrelation (Empirical)
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0 10 20 30 40
Yield1Yield2Yield3Yield4Yield5Yield6Yield7Yield8
Figs 6a to 6d
3.00
5.00
7.00
9.00
11.00
13.00
15.00
0 5 10 15 20 25 30
0360720108014401800
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
0 5 10 15 20 25 30
0360720108014401800
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
0 5 10 15 20 25 30
0360720108014401800
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00
13.00
0 5 10 15 20 25 30
0360720108014401800
Fig 7
Eigenvalues
0
0.0001
0.0002
0.0003
0.0004
0.0005
0.0006
0.0007
0.0008
0.0009
0 2 4 6 8 10
EmpiricalRandomSpringBox
Fig 8
First Eigenvector
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
01 2 3 4 5 6 7 8
EmpiricalRandomSpringBox
Fig 9
Second Eigenvector
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 2 3 4 5 6 7 8
EmpiricalRandomSpringBox
Fig 10
Third Eigenvector
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1 2 3 4 5 6 7 8
EmpiricalRandomSpringBox
Fig 11
Lag-1 Serial Autocorrelation (Random)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 10 20 30 40 50
Yield1
Yield2
Yield3
Yield4
Yield5
Yield6
Yield7
Yield8
Fig 12
Variance of Curvatures
- 0.00200 0.00400 0.00600 0.00800 0.01000 0.01200 0.01400 0.01600 0.01800 0.02000
0.625 1.25 3 6 12.5 20
Empirical
Random
Spring
Box
Fig 13
Lag-1 Serial Autocorrelation (Spring)
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0 10 20 30 40 50
Yield1
Yield2
Yield3
Yield4
Yield5
Yield6
Yield7
Yield8
Fig 14
Lag-1 Serial Autocorrelation (Box)
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
0 10 20 30 40
Yield1
Yield2
Yield3
Yield4
Yield5
Yield6
Yield7
Yield8
Fig 15a
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 10 20 30 40 50 60
DEPOSIT_USD_3M
Real World
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 10 20 30 40 50 60
DEPOSIT_USD_6M
Real World
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0 10 20 30 40 50 60
BOND_USD_2Y
Real World
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0.50
0.60
0.70
0 10 20 30 40 50 60
BOND_USD_5Y
Real World
Fig 15b
-0.20
-0.10
0.00
0.10
0.20
0.30
0.40
0 10 20 30 40 50 60
BOND_USD_20Y
Real World
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
0 10 20 30 40 50 60
BOND_USD_30Y
Real World
Fig 16a
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0 10 20 30 40 50 60 70
3m
Empirical
Box+Spring
Fig 16b
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0 10 20 30 40 50 60 70
6m
Empirical
Box+Spring
Fig 16c
0
0.005
0.01
0.015
0.02
0.025
0 10 20 30 40 50 60 70
1y
Empirical
Box+Spring
Fig 16d
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0 10 20 30 40 50 60 70
2y
Empirical
Box+Spring
Fig 16e
0
0.002
0.004
0.006
0.008
0.01
0.012
0.014
0.016
0.018
0.02
0 10 20 30 40 50 60 70
5y
Empirical
Box+Spring
Fig 16f
0
0.002
0.004
0.006
0.008
0.01
0.012
0 10 20 30 40 50 60 70
10y
Empirical
Box+Spring
Fig 16g
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 10 20 30 40 50 60 70
20y
Empirical
Box+Spring
Fig 16h
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0 10 20 30 40 50 60 70
30y
Empirical
Box+Spring
Figs 17 and 19
4
4.5
5
5.5
6
6.5
0 5 10 15 20 25 30
Series1Series2Series3Series4Series5
4
4.5
5
5.5
6
6.5
7
0 5 10 15 20 25 30
Series1Series2Series3Series4Series5
4
4.5
5
5.5
6
6.5
7
7.5
0 5 10 15 20 25 30
Series1Series2Series3Series4Series5
Fig 20
-0.60000
-0.50000
-0.40000
-0.30000
-0.20000
-0.10000
0.00000
0.10000
3m 6m 1y 2y 5y 10y 20y 30y
Percentage
Absolute
Tab 1
Levels of Rates
DEPOSIT_USD_3M
DEPOSIT_USD_6M
DEPOSIT_USD_1Y
BOND_USD_2Y
BOND_USD_5Y
BOND_USD_10Y
BOND_USD_20Y
BOND_USD_30Y
min 1.95% 1.92% 2.03% 2.33% 3.30% 4.24% 4.61% 5.08%max 6.88% 7.13% 7.81% 7.05% 8.31% 8.47% 8.46% 8.64%
average 5.37% 5.46% 5.66% 5.32% 5.84% 6.22% 6.39% 6.66%stdev 0.97% 0.99% 1.02% 1.01% 1.03% 0.86% 0.81% 0.80%
variance 9.38E-05 9.88E-05 0.0001045 0.0001011 0.0001051 7.44E-05 6.49E-05 6.44E-05skew -1.284865 -1.24616 -0.987848 -0.911544 -0.160438 0.3519517 0.424101 0.4300074kurt 1.5977754 1.688182 1.3741211 0.0593891 0.050623 -0.284676 -0.439583 -0.790756
Tab 2
Changes in Rates
DEPOSIT_USD_3M
DEPOSIT_USD_6M
DEPOSIT_USD_1Y
BOND_USD_2Y
BOND_USD_5Y
BOND_USD_10Y
BOND_USD_20Y
BOND_USD_30Y
min -10.61% -10.70% -12.13% -15.13% -8.50% -4.60% -6.23% -8.55%max 10.23% 8.11% 9.55% 9.42% 21.41% 5.42% 4.42% 3.83%
average -0.02% -0.02% -0.01% 0.01% 0.02% 0.00% 0.00% 0.00%stdev 0.88% 0.93% 1.10% 1.24% 1.28% 1.07% 0.92% 0.85%
variance 7.82E-05 8.69E-05 0.0001205 0.0001543 0.0001644 0.0001144 8.36E-05 7.25E-05skew -0.797953 -0.843082 -0.302394 -0.593901 2.2221474 0.2967838 0.1583266 -0.442658kurt 25.487472 18.893852 14.115295 15.139442 38.609994 2.1730483 2.4543888 6.0621243
Tab 3
Curvatures 3M -> 1Y 6M -> 2Y 1Y -> 5Y 2Y -> 10Y 5Y -> 20Y 10Y -> 30Y
min -0.04 -0.004292 -0.01516 -0.00098 -9.06E-05 -4.80E-05max 0.05 0.0503644 0.0021362 0.0024292 0.0006796 2.58E-05
average -0.000923 0.010068 -0.002584 0.0002376 7.97E-05 -1.04E-05stdev 0.0103632 0.010134 0.003329 0.000592 0.0001685 7.92E-06
variance 0.0001074 0.0001027 1.11E-05 3.51E-07 2.84E-08 6.27E-11skew 1.3151704 1.6675879 -1.673357 1.9059361 2.4168937 -0.211149kurt 4.1702147 2.1296391 2.0909057 4.5001319 4.6589933 0.6917889
Tab 4
Changes in Curvatures
3M -> 1Y 6M -> 2Y 1Y -> 5Y 2Y -> 10Y 5Y -> 20Y 10Y -> 30Y
min -0.061664 -0.008133 -0.002967 -0.000295 -0.000336 -4.94E-05max 0.0466667 0.0091731 0.0024167 0.0016959 4.67E-05 5.16E-05
average -6.62E-06 -2.86E-06 1.60E-06 7.41E-07 -2.03E-07 8.82E-09stdev 0.0048353 0.001637 0.0003536 5.10E-05 1.02E-05 2.00E-06
variance 2.34E-05 2.68E-06 1.25E-07 2.60E-09 1.05E-10 4.00E-12skew -1.001259 0.1252825 -0.076296 16.993317 -16.63672 0.9629592kurt 22.543064 2.541568 5.7177958 574.98034 539.3809 404.26392
Tab 5
Empirical Random Spring Box0.625 0.00999 0.01829 0.00850 0.00782 1.25 0.00431 0.01278 0.00217 0.00536
3 0.00095 0.00366 0.00097 0.00126 6 0.00027 0.00122 0.00015 0.00041
12.5 0.00006 0.00040 0.00005 0.00008 20 0.00003 0.00015 0.00002 0.00002
Tab 6
Percentage Absolute3m -0.25930 0.042276m -0.35212 0.018891y -0.47963 -0.056702y -0.48984 -0.089825y -0.39558 -0.1271810y -0.25171 -0.0709820y -0.12260 0.0065530y -0.06846 0.01371