ycextra: Yield curve or zero-coupon prices extrapolation
In ycinterextra: Yield curve or zero-coupon prices interpolation and extrapolation
Description
Usage
Arguments
Details
Value
Author(s)
See Also
Examples
Description
Yield curve or zero-coupon bonds prices curve
extrapolation using the Nelson-Siegel, Svensson,
Smith-Wilson models.
Usage
1
2
3
Arguments
yM
A vector of non-negative numerical quantities,
containing the yield to maturities.
p
A vector of non-negative numerical quantities,
containing the zero-coupon prices.
matsin
A vector containing the observed
maturities.
matsout
the output maturities needed.
method
A character string giving the type of
method used fo intepolation and extrapolation. method can be either
"NS" for Nelson-Siegel, "SV" for Svensson, or "SW" Smith-Wilson.
typeres
A character string, giving the type of
return. Either "prices" or "rates".
UFR
The ultimate forward rate.
T_UFR
The number of years after which the yield
curve converges to the UFR. T_UFR is used only
when method is "SW".
Details
This function interpolates between observed points of a
yield curve, or zero-coupon prices, and extrapolates the
curve using the Nelson-Siegel, Svensson, Smith-Wilson
models. The result can be either prices or zero rates.
For the purpose of extrapolation, an ultimate forward
rate (UFR) to which the yield curve converges must be
provided. With the Smith-Wilson method, a period of
convergence (number of years) to the ultimate forward
rate, after the last liquid point, must be provided.
Value
An S4 Object, that can be easily converted into a list with
as.list
Author(s)
Thierry Moudiki
See Also
Examples
1
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# 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)
# 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 = 60, by = 0.5)
# Svensson extrapolation
yc <- ycextra(p = p, matsin = u, matsout = t,
method="SV", typeres="prices", UFR = 0.018)
ycsummary(yc)
#Smith-Wilson extrapolation
yc <- ycextra(p = p, matsin = u, matsout = t,
method="SW", typeres="rates", UFR = 0.019, T_UFR = 20)
ycsummary(yc)
# Nelson-Siegel extrapolation
yc <- ycextra(yM = txZC, matsin = u, matsout = t,
method="NS", typeres="prices", UFR = 0.029)
ycsummary(yc)
Example output
Loading required package: compiler
Attaching package: 'ycinterextra'
The following objects are masked from 'package:stats':
deviance, fitted, residuals
The following object is masked from 'package:base':
as.list
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Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-1.476e-03 -8.560e-04 -3.911e-05 2.248e-05 6.715e-04 2.011e-03
Coefficients:
0.018 -0.0005215511 -0.06880811 0.07883251 2.751234 5.489952
Total sum of squares:
0.539461
with 29 degrees of freedom
Explained sum of squares:
0.5394328
with 5 degrees of freedom
Residual sum of squares:
2.825367e-05
with 24 degrees of freedom
Multiple R-squared * Adjusted R-squared
0.9999476 * 0.9999367
F-statistic: 91643.93 on 24 and 5 degrees of freedom, p-value: 1
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.365e-14 1.031e-13 1.092e-13 1.037e-13 1.127e-13 1.278e-13
Coefficients:
0.138 -5.424536 3.32294 0.7830358 0.1401277 0.4016121 -0.4496507 -0.698104 0.300638 -0.2192093 0.3006983 0.09682321 0.02404538 -0.4186581 0.1891097 -0.2564345 0.01311163 0.3146892 -0.7371963 0.6173576 -0.4226662 0.5335023 -0.4937284 0.4974411 -0.5775822 0.2187933 0.1117317 -0.1689916 -0.08575088 -0.2268892 0.5487419
Total sum of squares:
0.5390404
with 29 degrees of freedom
Explained sum of squares:
0.5390404
with 29 degrees of freedom
Residual sum of squares:
3.381638e-25
with 0 degrees of freedom
Multiple R-squared * Adjusted R-squared
1 * NaN
F-statistic: NaN on 0 and 29 degrees of freedom, p-value: NaN
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Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.0016902 -0.0007469 0.0001696 0.0002078 0.0012895 0.0019596
Coefficients:
0.029 0.0100502 -0.07201655 0.8132519
Total sum of squares:
0.0005819048
with 29 degrees of freedom
Explained sum of squares:
0.0005379112
with 3 degrees of freedom
Residual sum of squares:
4.399356e-05
with 26 degrees of freedom
Multiple R-squared * Adjusted R-squared
0.9243973 * 0.9156739
F-statistic: 105.9677 on 26 and 3 degrees of freedom, p-value: 0.9987092
ycinterextra documentation built on May 1, 2019, 8:02 p.m.
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Description Usage Arguments Details Value Author(s) See Also Examples
Description
Yield curve or zero-coupon bonds prices curve extrapolation using the Nelson-Siegel, Svensson, Smith-Wilson models.
Usage
1 2 3 |
Arguments
yM |
A vector of non-negative numerical quantities, containing the yield to maturities. |
p |
A vector of non-negative numerical quantities, containing the zero-coupon prices. |
matsin |
A vector containing the observed maturities. |
matsout |
the output maturities needed. |
method |
A character string giving the type of
method used fo intepolation and extrapolation. |
typeres |
A character string, giving the type of return. Either "prices" or "rates". |
UFR |
The ultimate forward rate. |
T_UFR |
The number of years after which the yield
curve converges to the UFR. |
Details
This function interpolates between observed points of a yield curve, or zero-coupon prices, and extrapolates the curve using the Nelson-Siegel, Svensson, Smith-Wilson models. The result can be either prices or zero rates. For the purpose of extrapolation, an ultimate forward rate (UFR) to which the yield curve converges must be provided. With the Smith-Wilson method, a period of convergence (number of years) to the ultimate forward rate, after the last liquid point, must be provided.
Value
An S4 Object, that can be easily converted into a list with
as.list
Author(s)
Thierry Moudiki
See Also
Examples
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 27 28 29 30 31 32 33 | # 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)
# 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 = 60, by = 0.5)
# Svensson extrapolation
yc <- ycextra(p = p, matsin = u, matsout = t,
method="SV", typeres="prices", UFR = 0.018)
ycsummary(yc)
#Smith-Wilson extrapolation
yc <- ycextra(p = p, matsin = u, matsout = t,
method="SW", typeres="rates", UFR = 0.019, T_UFR = 20)
ycsummary(yc)
# Nelson-Siegel extrapolation
yc <- ycextra(yM = txZC, matsin = u, matsout = t,
method="NS", typeres="prices", UFR = 0.029)
ycsummary(yc)
|
Example output
Loading required package: compiler
Attaching package: 'ycinterextra'
The following objects are masked from 'package:stats':
deviance, fitted, residuals
The following object is masked from 'package:base':
as.list
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Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-1.476e-03 -8.560e-04 -3.911e-05 2.248e-05 6.715e-04 2.011e-03
Coefficients:
0.018 -0.0005215511 -0.06880811 0.07883251 2.751234 5.489952
Total sum of squares:
0.539461
with 29 degrees of freedom
Explained sum of squares:
0.5394328
with 5 degrees of freedom
Residual sum of squares:
2.825367e-05
with 24 degrees of freedom
Multiple R-squared * Adjusted R-squared
0.9999476 * 0.9999367
F-statistic: 91643.93 on 24 and 5 degrees of freedom, p-value: 1
Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
2.365e-14 1.031e-13 1.092e-13 1.037e-13 1.127e-13 1.278e-13
Coefficients:
0.138 -5.424536 3.32294 0.7830358 0.1401277 0.4016121 -0.4496507 -0.698104 0.300638 -0.2192093 0.3006983 0.09682321 0.02404538 -0.4186581 0.1891097 -0.2564345 0.01311163 0.3146892 -0.7371963 0.6173576 -0.4226662 0.5335023 -0.4937284 0.4974411 -0.5775822 0.2187933 0.1117317 -0.1689916 -0.08575088 -0.2268892 0.5487419
Total sum of squares:
0.5390404
with 29 degrees of freedom
Explained sum of squares:
0.5390404
with 29 degrees of freedom
Residual sum of squares:
3.381638e-25
with 0 degrees of freedom
Multiple R-squared * Adjusted R-squared
1 * NaN
F-statistic: NaN on 0 and 29 degrees of freedom, p-value: NaN
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Residuals:
Min. 1st Qu. Median Mean 3rd Qu. Max.
-0.0016902 -0.0007469 0.0001696 0.0002078 0.0012895 0.0019596
Coefficients:
0.029 0.0100502 -0.07201655 0.8132519
Total sum of squares:
0.0005819048
with 29 degrees of freedom
Explained sum of squares:
0.0005379112
with 3 degrees of freedom
Residual sum of squares:
4.399356e-05
with 26 degrees of freedom
Multiple R-squared * Adjusted R-squared
0.9243973 * 0.9156739
F-statistic: 105.9677 on 26 and 3 degrees of freedom, p-value: 0.9987092
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