ycextra: Yield curve or zero-coupon prices extrapolation

Description

Yield curve or zero-coupon bonds prices curve extrapolation using the Nelson-Siegel, Svensson, Smith-Wilson models.

Usage

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

Arguments

A vector of non-negative numerical quantities, containing the yield to maturities.

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".

Value

An S4 Object, that can be easily converted into a list with as.list

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.

Examples

Run this code

# 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)