ycinter.RdYield curve or zero-coupon bonds prices curve interpolation using the Nelson-Siegel , Svensson, Smith-Wilson models and an Hermite cubic spline.
A vector of non-negative numerical quantities, containing the yield to maturities.
A vector of non-negative numerical quantities, containing the zero-coupon prices.
A vector containing the observed maturities.
the output maturities needed.
A character string giving the type of
method used fo intepolation. method can be either
"NS" for Nelson-Siegel, "SV" for Svensson, "HCSPL" for
Hermite cubic spline, or "SW" Smith-Wilson.
A character string, giving the type of return. Either "prices" or "rates".
An S4 Object
This function interpolates between observed points of a yield curve, or zero-coupon prices, using the Nelson-Siegel, Svensson, Smith-Wilson models and an Hermite cubic spline. The result can be either prices or zero rates.
## Interpolation of yields to matuities with prices as outputs
# Yield to maturities
txZC <- c(0.01422,0.01309,0.01380,0.01549,0.01747,0.01940,0.02104,0.02236,0.02348,
0.02446,0.02535,0.02614,0.02679,0.02727,0.02760,0.02779,0.02787,0.02786,0.02776
,0.02762,0.02745,0.02727,0.02707,0.02686,0.02663,0.02640,0.02618,0.02597,0.02578,0.02563)
# Zero-coupon prices
p <- c(0.9859794,0.9744879,0.9602458,0.9416551,0.9196671,0.8957363,0.8716268,0.8482628,
0.8255457,0.8034710,0.7819525,0.7612204,0.7416912,0.7237042,0.7072136
,0.6922140,0.6785227,0.6660095,0.6546902,0.6441639,0.6343366,0.6250234,0.6162910,0.6080358,
0.6003302,0.5929791,0.5858711,0.5789852,0.5722068,0.5653231)
# Observed maturities
u <- 1:30
# Output maturities
t <- seq(from = 1, to = 30, by = 0.5)
# Cubic splines interpolation
(yc <- ycinter(yM = txZC, matsin = u, matsout = t,
method="HCSPL", typeres="rates"))
#> An object of class "ycInterExtra"
#> Slot "matsin":
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
#> [26] 26 27 28 29 30
#>
#> Slot "observedvalues":
#> [1] 0.01422 0.01309 0.01380 0.01549 0.01747 0.01940 0.02104 0.02236 0.02348
#> [10] 0.02446 0.02535 0.02614 0.02679 0.02727 0.02760 0.02779 0.02787 0.02786
#> [19] 0.02776 0.02762 0.02745 0.02727 0.02707 0.02686 0.02663 0.02640 0.02618
#> [28] 0.02597 0.02578 0.02563
#>
#> Slot "method":
#> [1] "HCSPL"
#>
#> Slot "typeres":
#> [1] "rates"
#>
#> Slot "coefficients":
#> [1] NA
#>
#> Slot "matsout":
#> [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
#> [16] 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
#> [31] 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0
#> [46] 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0
#>
#> Slot "fittedvalues":
#> [1] 0.01422000 0.01324875 0.01309000 0.01326875 0.01380000 0.01456562
#> [7] 0.01549000 0.01646500 0.01747000 0.01845625 0.01940000 0.02025813
#> [13] 0.02104000 0.02173250 0.02236000 0.02294125 0.02348000 0.02398437
#> [19] 0.02446000 0.02491688 0.02535000 0.02576000 0.02614000 0.02648438
#> [25] 0.02679000 0.02705000 0.02727000 0.02745313 0.02760000 0.02771062
#> [31] 0.02779000 0.02784250 0.02787000 0.02787625 0.02786000 0.02781812
#> [37] 0.02776000 0.02769437 0.02762000 0.02753750 0.02745000 0.02736187
#> [43] 0.02727000 0.02717188 0.02707000 0.02696688 0.02686000 0.02674625
#> [49] 0.02663000 0.02651438 0.02640000 0.02628875 0.02618000 0.02607313
#> [55] 0.02597000 0.02587125 0.02578000 0.02568375 0.02563000
#>
#> Slot "residuals":
#> [1] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
#>
#> Slot "fwdrates":
#> [1] 0.01114773 0.01236796 0.01362700 0.01592789 0.01839771 0.02089538
#> [7] 0.02284926 0.02468596 0.02604382 0.02703676 0.02736978 0.02757355
#> [13] 0.02739305 0.02731958 0.02734905 0.02731275 0.02729512 0.02728088
#> [19] 0.02736170 0.02730254 0.02719631 0.02690860 0.02645193 0.02586718
#> [25] 0.02507658 0.02432655 0.02357874 0.02278811 0.02194440 0.02116146
#> [31] 0.02043589 0.01971870 0.01905886 0.01834294 0.01752313 0.01690795
#> [37] 0.01649860 0.01605112 0.01561292 0.01525229 0.01500880 0.01468215
#> [43] 0.01428452 0.01395438 0.01369591 0.01336634 0.01294280 0.01264663
#> [49] 0.01244672 0.01227055 0.01215830 0.01203326 0.01189428 0.01182178
#> [55] 0.01177728 0.01184504 0.01150207 0.01277756
#>
#> Slot "UFR":
#> numeric(0)
#>
#> Slot "T_UFR":
#> numeric(0)
#>
#> Slot "extrapvalues":
#> logical(0)
#>
# Nelson-Siegel interpolation
(yc <- ycinter(yM = txZC, matsin = u, matsout = t,
method="NS", typeres="prices"))
#>
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#> An object of class "ycInterExtra"
#> Slot "matsin":
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
#> [26] 26 27 28 29 30
#>
#> Slot "observedvalues":
#> [1] 0.01422 0.01309 0.01380 0.01549 0.01747 0.01940 0.02104 0.02236 0.02348
#> [10] 0.02446 0.02535 0.02614 0.02679 0.02727 0.02760 0.02779 0.02787 0.02786
#> [19] 0.02776 0.02762 0.02745 0.02727 0.02707 0.02686 0.02663 0.02640 0.02618
#> [28] 0.02597 0.02578 0.02563
#>
#> Slot "method":
#> [1] "NS"
#>
#> Slot "typeres":
#> [1] "prices"
#>
#> Slot "coefficients":
#> [1] 0.029835218 0.002110268 -0.062475115 0.965939606
#>
#> Slot "matsout":
#> [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
#> [16] 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
#> [31] 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0
#> [46] 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0
#>
#> Slot "fittedvalues":
#> [1] 0.9857842 0.9817232 0.9761104 0.9686163 0.9595058 0.9492104 0.9381439
#> [8] 0.9266404 0.9149455 0.9032299 0.8916061 0.8801459 0.8688921 0.8578691
#> [15] 0.8470885 0.8365545 0.8262661 0.8162195 0.8064092 0.7968289 0.7874716
#> [22] 0.7783304 0.7693982 0.7606683 0.7521340 0.7437889 0.7356269 0.7276420
#> [29] 0.7198286 0.7121811 0.7046944 0.6973635 0.6901836 0.6831499 0.6762582
#> [36] 0.6695041 0.6628837 0.6563928 0.6500279 0.6437852 0.6376613 0.6316527
#> [43] 0.6257564 0.6199691 0.6142879 0.6087098 0.6032322 0.5978523 0.5925674
#> [50] 0.5873752 0.5822732 0.5772591 0.5723305 0.5674855 0.5627217 0.5580373
#> [57] 0.5534302 0.5488986 0.5444406
#>
#> Slot "residuals":
#> [1] -2.008384e-04 8.528822e-04 -2.677122e-04 -9.936290e-04 -1.122245e-03
#> [6] -8.619111e-04 -5.158333e-04 -2.042691e-04 1.173417e-04 4.534822e-04
#> [11] 8.148137e-04 1.163577e-03 1.439978e-03 1.599662e-03 1.652023e-03
#> [16] 1.599078e-03 1.464710e-03 1.264159e-03 9.936659e-04 7.002218e-04
#> [21] 3.913914e-04 8.518191e-05 -2.300529e-04 -5.456847e-04 -8.728661e-04
#> [26] -1.192572e-03 -1.495633e-03 -1.782761e-03 -2.044570e-03 -2.261591e-03
#>
#> Slot "fwdrates":
#> [1] 0.007615291 0.009749606 0.013786989 0.017841024 0.021239063 0.023849331
#> [7] 0.025753652 0.027096345 0.028020362 0.028644826 0.029060952 0.029335148
#> [13] 0.029514171 0.029630167 0.029704840 0.029752646 0.029783105 0.029802431
#> [19] 0.029814647 0.029822344 0.029827180 0.029830209 0.029832103 0.029833284
#> [25] 0.029834019 0.029834476 0.029834759 0.029834935 0.029835043 0.029835110
#> [31] 0.029835152 0.029835177 0.029835193 0.029835203 0.029835209 0.029835212
#> [37] 0.029835214 0.029835216 0.029835217 0.029835217 0.029835217 0.029835218
#> [43] 0.029835218 0.029835218 0.029835218 0.029835218 0.029835218 0.029835218
#> [49] 0.029835218 0.029835218 0.029835218 0.029835218 0.029835218 0.029835218
#> [55] 0.029835218 0.029835218 0.029835218 0.029835218 0.029835218
#>
#> Slot "UFR":
#> numeric(0)
#>
#> Slot "T_UFR":
#> numeric(0)
#>
#> Slot "extrapvalues":
#> logical(0)
#>
# Svensson interpolation
(yc <- ycinter(p = p, matsin = u, matsout = t,
method="SV", typeres="prices"))
#>
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#> An object of class "ycInterExtra"
#> Slot "matsin":
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
#> [26] 26 27 28 29 30
#>
#> Slot "observedvalues":
#> [1] 0.9859794 0.9744879 0.9602458 0.9416551 0.9196671 0.8957363 0.8716268
#> [8] 0.8482628 0.8255457 0.8034710 0.7819525 0.7612204 0.7416912 0.7237042
#> [15] 0.7072136 0.6922140 0.6785227 0.6660095 0.6546902 0.6441639 0.6343366
#> [22] 0.6250234 0.6162910 0.6080358 0.6003302 0.5929791 0.5858711 0.5789852
#> [29] 0.5722068 0.5653231
#>
#> Slot "method":
#> [1] "SV"
#>
#> Slot "typeres":
#> [1] "prices"
#>
#> Slot "coefficients":
#> [1] 0.0167490974 0.0007332705 -0.0587944840 0.0726161792 2.6314268408
#> [6] 6.0000000000
#>
#> Slot "matsout":
#> [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
#> [16] 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
#> [31] 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0
#> [46] 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0
#>
#> Slot "fittedvalues":
#> [1] 0.9861237 0.9802397 0.9740930 0.9673005 0.9596633 0.9511152 0.9416815
#> [8] 0.9314478 0.9205351 0.9090815 0.8972288 0.8851135 0.8728609 0.8605819
#> [15] 0.8483716 0.8363094 0.8244597 0.8128730 0.8015875 0.7906311 0.7800225
#> [22] 0.7697729 0.7598875 0.7503663 0.7412055 0.7323982 0.7239351 0.7158053
#> [29] 0.7079967 0.7004963 0.6932907 0.6863663 0.6797095 0.6733069 0.6671452
#> [36] 0.6612117 0.6554940 0.6499804 0.6446595 0.6395204 0.6345529 0.6297473
#> [43] 0.6250943 0.6205853 0.6162121 0.6119670 0.6078428 0.6038325 0.5999299
#> [50] 0.5961290 0.5924241 0.5888100 0.5852817 0.5818347 0.5784647 0.5751675
#> [57] 0.5719395 0.5687771 0.5656770
#>
#> Slot "residuals":
#> [1] -1.443340e-04 3.949105e-04 5.824680e-04 -2.643971e-05 -8.680450e-04
#> [6] -1.492532e-03 -1.234084e-03 -1.087951e-04 1.085985e-03 1.883505e-03
#> [11] 1.930005e-03 1.332886e-03 4.857046e-04 -2.308814e-04 -7.831032e-04
#> [16] -1.076727e-03 -1.186827e-03 -1.135667e-03 -8.038416e-04 -4.955561e-04
#> [21] -2.162725e-04 -7.089419e-05 7.886870e-05 1.930379e-04 4.002657e-04
#> [26] 5.550020e-04 5.893735e-04 5.205415e-04 2.673179e-04 -3.538680e-04
#>
#> Slot "fwdrates":
#> [1] 0.01221594 0.01234931 0.01353852 0.01537775 0.01756964 0.01990023
#> [7] 0.02221921 0.02442456 0.02645044 0.02825793 0.02982776 0.03115478
#> [13] 0.03224373 0.03310601 0.03375728 0.03421570 0.03450057 0.03463140
#> [19] 0.03462729 0.03450646 0.03428596 0.03398153 0.03360750 0.03317678
#> [25] 0.03270092 0.03219013 0.03165339 0.03109852 0.03053227 0.02996047
#> [31] 0.02938805 0.02881918 0.02825735 0.02770541 0.02716572 0.02664014
#> [37] 0.02613013 0.02563680 0.02516096 0.02470315 0.02426371 0.02384275
#> [43] 0.02344028 0.02305612 0.02269003 0.02234165 0.02201056 0.02169629
#> [49] 0.02139833 0.02111611 0.02084906 0.02059660 0.02035814 0.02013306
#> [55] 0.01992078 0.01972072 0.01953228 0.01935490 0.01918803
#>
#> Slot "UFR":
#> numeric(0)
#>
#> Slot "T_UFR":
#> numeric(0)
#>
#> Slot "extrapvalues":
#> logical(0)
#>
#Smith-Wilson interpolation
(yc <- ycinter(p = p, matsin = u, matsout = t,
method="SW", typeres="rates"))
#> An object of class "ycInterExtra"
#> Slot "matsin":
#> [1] 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
#> [26] 26 27 28 29 30
#>
#> Slot "observedvalues":
#> [1] 0.9859794 0.9744879 0.9602458 0.9416551 0.9196671 0.8957363 0.8716268
#> [8] 0.8482628 0.8255457 0.8034710 0.7819525 0.7612204 0.7416912 0.7237042
#> [15] 0.7072136 0.6922140 0.6785227 0.6660095 0.6546902 0.6441639 0.6343366
#> [22] 0.6250234 0.6162910 0.6080358 0.6003302 0.5929791 0.5858711 0.5789852
#> [29] 0.5722068 0.5653231
#>
#> Slot "method":
#> [1] "SW"
#>
#> Slot "typeres":
#> [1] "rates"
#>
#> Slot "coefficients":
#> alpha Xhi1 Xhi2 Xhi3 Xhi4 Xhi5
#> 0.1000000 -16.2793106 9.2018018 2.2913598 0.5161016 1.5037057
#> Xhi6 Xhi7 Xhi8 Xhi9 Xhi10 Xhi11
#> -1.3223252 -2.5025163 1.1148478 -0.8738030 1.2481411 0.5236537
#> Xhi12 Xhi13 Xhi14 Xhi15 Xhi16 Xhi17
#> 0.2688466 -1.9200691 0.9839525 -1.2894406 0.0207775 1.9120039
#> Xhi18 Xhi19 Xhi20 Xhi21 Xhi22 Xhi23
#> -4.4858109 3.7900455 -2.8174232 3.6735880 -3.5512650 3.7663330
#> Xhi24 Xhi25 Xhi26 Xhi27 Xhi28 Xhi29
#> -4.5201320 1.4824788 1.4760939 -3.6049755 6.7996513 -33.0482736
#> Xhi30
#> 31.9270982
#>
#> Slot "matsout":
#> [1] 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0
#> [16] 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 15.5
#> [31] 16.0 16.5 17.0 17.5 18.0 18.5 19.0 19.5 20.0 20.5 21.0 21.5 22.0 22.5 23.0
#> [46] 23.5 24.0 24.5 25.0 25.5 26.0 26.5 27.0 27.5 28.0 28.5 29.0 29.5 30.0
#>
#> Slot "fittedvalues":
#> [1] 0.01421997 0.01346760 0.01309000 0.01325935 0.01380001 0.01457830
#> [7] 0.01548999 0.01646886 0.01747000 0.01845983 0.01940000 0.02026288
#> [13] 0.02104000 0.02173247 0.02235999 0.02294033 0.02348000 0.02398364
#> [19] 0.02446000 0.02491575 0.02535001 0.02575977 0.02614000 0.02648535
#> [25] 0.02679000 0.02705030 0.02727000 0.02745315 0.02760000 0.02771091
#> [31] 0.02779000 0.02784174 0.02787000 0.02787699 0.02786000 0.02781807
#> [37] 0.02776000 0.02769403 0.02762000 0.02753721 0.02745001 0.02736187
#> [43] 0.02727000 0.02717180 0.02707000 0.02696701 0.02686000 0.02674660
#> [49] 0.02663000 0.02651391 0.02640000 0.02628898 0.02618000 0.02607273
#> [55] 0.02597000 0.02587369 0.02578000 0.02569033 0.02563000
#>
#> Slot "residuals":
#> [1] -3.774758e-13 -7.217560e-13 -1.066702e-12 -1.375788e-12 -1.644573e-12
#> [6] -1.948997e-12 -2.210343e-12 -2.430167e-12 -2.791545e-12 -2.826850e-12
#> [11] -2.958522e-12 -3.067879e-12 -3.121059e-12 -3.217870e-12 -3.239298e-12
#> [16] -3.284484e-12 -3.292921e-12 -3.317902e-12 -3.330558e-12 -3.342993e-12
#> [21] -3.359868e-12 -3.318346e-12 -3.281597e-12 -3.246625e-12 -3.200440e-12
#> [26] -3.148592e-12 -3.089862e-12 -3.025580e-12 -2.953859e-12 -2.880696e-12
#>
#> Slot "fwdrates":
#> [1] 0.01179513 0.01172045 0.01358118 0.01597380 0.01848283 0.02081001
#> [7] 0.02288206 0.02465319 0.02608013 0.02700047 0.02742520 0.02751815
#> [13] 0.02739260 0.02731992 0.02733591 0.02732596 0.02728367 0.02729236
#> [19] 0.02734270 0.02732165 0.02719214 0.02691264 0.02647055 0.02584860
#> [25] 0.02508263 0.02432051 0.02357922 0.02278754 0.02195077 0.02115508
#> [31] 0.02041851 0.01973620 0.01907627 0.01832558 0.01752159 0.01690937
#> [37] 0.01648977 0.01605987 0.01560545 0.01525998 0.01500841 0.01468253
#> [43] 0.01428227 0.01395663 0.01369977 0.01336237 0.01295313 0.01263624
#> [49] 0.01243248 0.01228495 0.01216557 0.01202600 0.01188136 0.01183444
#> [55] 0.01185783 0.01176455 0.01172425 0.01255530
#>
#> Slot "UFR":
#> numeric(0)
#>
#> Slot "T_UFR":
#> numeric(0)
#>
#> Slot "extrapvalues":
#> logical(0)
#>