YieldCurve (version 4.1)

Nelson.Siegel: Estimation of the Nelson-Siegel parameters

Description

Returns the estimated coefficients of the Nelson-Siegel's model.

Usage

Nelson.Siegel( rate, maturity )

Arguments

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.

Value

• Returns a data frame with the estimated coefficients: $\beta_{0t}$, $\beta_{1t}$, $\beta_{2t}$, and $\lambda$.

Details

The Nelson-Siegel's model to describe the yield curve is: $$y_t(\tau) = \beta_{0t} + \beta_{1t} \frac{1-\exp(-\lambda \tau)}{\lambda \tau} + \beta_{2t} \left(\frac{1-\exp(-\lambda \tau)}{\lambda \tau} - \exp(-\lambda \tau) \right)$$

References

Diebold, F.X. and Li, C. (2006), Forecasting the Term Structure of Government Bond Yields, Journal of Econometrics, 130, 337-364.

Diebold, F.X., Ji, L. and Li, C. (2006), A Three-Factor Yield Curve Model: Non-Affine Structure, Systematic Risk Sources, and Generalized Duration, in L.R. Klein (ed.), Long-Run Growth and Short-Run Stabilization: Essays in Memory of Albert Ando. Cheltenham, U.K.: Edward Elgar, 240-274.

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

See Also

NelsonSiegel, Svensson

Examples

data(FedYieldCurve)
maturity.Fed <- c(3/12, 0.5, 1,2,3,5,7,10)
NSParameters <- Nelson.Siegel( rate=first(FedYieldCurve,'10 month'),	maturity=maturity.Fed)
y <- NSrates(NSParameters[5,], maturity.Fed)
plot(maturity.Fed,FedYieldCurve[5,],main="Fitting Nelson-Siegel yield curve",
  xlab=c("Pillars in months"), type="o")
lines(maturity.Fed,y, col=2)
legend("topleft",legend=c("observed yield curve","fitted yield curve"),
col=c(1,2),lty=1)
grid()