Svensson: Estimation of the Svensson parameters
In YieldCurve: Modelling and estimation of the yield curve

Description Usage Arguments Details Value Author(s) References Examples

Returns the estimated coefficients of the Svensson's model.

1	Svensson(rate, maturity )

`rate`	vector or matrix which contains the interest rates.
`maturity`	vector wich contains the maturity ( in months) of the `rate`. The vector's length must be the same of the number of columns of the `rate`.

The Svensson's model to describe the forward rate is:

y_t(τ) = β_{0} + β_{1} \exp≤ft( -\frac{τ}{λ_1} \right) + β_2 \frac{τ}{λ_1} \exp ≤ft( -\frac{τ}{λ_1} \right) + β_3 \frac{τ}{λ_2} \exp ≤ft( -\frac{τ}{λ_2} \right)

The spot rate can be derived from forward rate and it is given by:

y_t(τ) = β_0 + β_1 \frac{ 1- \exp( -\frac{τ}{λ_1}) }{\frac{τ}{λ_1} } + β_2 ≤ft[\frac{ 1- \exp( -\frac{τ}{λ_1}) }{\frac{τ}{λ_1} } - \exp( -\frac{τ}{λ_1}) \right] + β_3 ≤ft[\frac{ 1- \exp(-\frac{τ}{λ_2}) }{\frac{τ}{λ_2} } - \exp( -\frac{τ}{λ_2}) \right]

Returns a data frame with the estimated coefficients: β_{0}, β_{1}, β_{2},β_{3}, λ_1 and λ_2.

Sergio Salvino Guirreri

Svensson, L.E. (1994), Estimating and Interpreting Forward Interest Rates: Sweden 1992-1994, IMF Working Paper, WP/94/114.

Nelson, C.R., and A.F. Siegel (1987), Parsimonious Modeling of Yield Curve, The Journal of Business, 60, 473-489.

data(ECBYieldCurve)
maturity.ECB <- c(0.25,0.5,seq(1,30,by=1))
A <- Svensson(ECBYieldCurve[1:10,], maturity.ECB )
Svensson.rate <- Srates( A, maturity.ECB, "Spot" )
plot(maturity.ECB, Svensson.rate[5,],main="Fitting Svensson yield curve",
 xlab=c("Pillars in years"), type="l", col=3)
lines( maturity.ECB, ECBYieldCurve[5,],col=2)
legend("topleft",legend=c("fitted yield curve","observed yield curve"),
col=c(3,2),lty=1)
grid()

Loading required package: xts
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric