Svensson {YieldCurve} | 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 |
Details
The Svensson's model to describe the forward rate is:
y_t(\tau) = \beta_{0} + \beta_{1} \exp\left( -\frac{\tau}{\lambda_1} \right) + \beta_2
\frac{\tau}{\lambda_1} \exp \left( -\frac{\tau}{\lambda_1} \right) + \beta_3
\frac{\tau}{\lambda_2} \exp \left( -\frac{\tau}{\lambda_2} \right)
The spot rate can be derived from forward rate and it is given by:
y_t(\tau) = \beta_0 + \beta_1 \frac{ 1- \exp(
-\frac{\tau}{\lambda_1}) }{\frac{\tau}{\lambda_1} } + \beta_2 \left[\frac{ 1- \exp(
-\frac{\tau}{\lambda_1}) }{\frac{\tau}{\lambda_1} } - \exp( -\frac{\tau}{\lambda_1})
\right]
+ \beta_3 \left[\frac{ 1- \exp(-\frac{\tau}{\lambda_2}) }{\frac{\tau}{\lambda_2} } -
\exp( -\frac{\tau}{\lambda_2})
\right]
Value
Returns a data frame with the estimated coefficients: \beta_{0}
, \beta_{1}
, \beta_{2}
,\beta_{3}
, \lambda_1
and \lambda_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()