Svensson: Estimation of the Svensson parameters In YieldCurve: Modelling and Estimation of the Yield Curve

 Svensson R Documentation

Estimation of the Svensson parameters

Description

Returns the estimated coefficients of the Svensson's model.

Usage

Svensson(rate, maturity )

Arguments

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

Details

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]

Value

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

Author(s)

Sergio Salvino Guirreri

References

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.

Examples

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()

YieldCurve documentation built on Oct. 2, 2022, 5:08 p.m.