ycextra: Yield curve or zero-coupon prices 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

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  ycextra(yM = NULL, p = NULL, matsin, matsout,
    method = c("NS", "SV", "SW"),
    typeres = c("rates", "prices"), UFR, T_UFR = NULL)

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

ycsummary

Examples

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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.