Svensson | R Documentation |
Returns the estimated coefficients of the Svensson's model.
Svensson(rate, maturity )
rate |
vector or matrix which contains the interest rates. |
maturity |
vector which contains the maturity (in months) of the |
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()
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