NMOF (version 0.22-0)

NS: Zero Rates for Nelson--Siegel--Svensson Model

Description

Compute zero yields for Nelson--Siegel (NS)/Nelson--Siegel--Svensson (NSS) model.

Usage

NS(param, tm)
NSS(param, tm)

Arguments

param

a vector. For NS: $\beta_1$, $\beta_2$, $\beta_3$, $\lambda$. For NSS: a vector: $\beta_1$, $\beta_2$, $\beta_3$, $\beta_4$, $\lambda_1$, $\lambda_2$.

tm

a vector of maturities

Value

• The function returns a vector of length length(tm).

Details

See Chapter 14 in Gilli/Maringer/Schumann (2011). Maturities (tm) need to be given in time (not dates).

References

Gilli, M. and Grosse, S. and Schumann, E. (2010) Calibrating the Nelson-Siegel-Svensson model, COMISEF Working Paper Series No. 031. http://comisef.eu/files/wps031.pdf Gilli, M., Maringer, D. and Schumann, E. (2011) Numerical Methods and Optimization in Finance. Elsevier. http://www.elsevierdirect.com/product.jsp?isbn=9780123756626 Gilli, M. and Schumann, E. (2010) A Note on Good Starting Values in Numerical Optimisation, COMISEF Working Paper Series No. 044. http://comisef.eu/files/wps044.pdf Nelson, C.R. and Siegel, A.F. (1987) Parsimonious Modeling of Yield Curves. Journal of Business, 60(4), pp. 473--489. Svensson, L.E. (1994) Estimating and Interpreting Forward Interest Rates: Sweden 1992--1994. IMF Working Paper 94/114.

See Also

NSf, NSSf

Examples

tm <- c(c(1, 3, 6, 9) / 12, 1:10)  ### in years
param <- c(6, 3, 8, 1)
yM <- NS(param, tm)
plot(tm, yM, xlab = "maturity in years", 
             ylab = "yield in percent")

param <- c(6, 3, 5, -5, 1, 3)  
yM <- NSS(param, tm) 
plot(tm, yM, xlab = "maturity in years", 
             ylab = "yield in percent")


## get Bliss/Diebold/Li data (used in some of the papers in References)
u <- url("http://www.ssc.upenn.edu/~fdiebold/papers/paper49/FBFITTED.txt")
open(u); BliDiLi <- scan(u, skip = 14); close(u)
mat <- NULL
for (i in 1:372) 
    mat <- rbind(mat,BliDiLi[(19*(i-1)+1):(19*(i-1)+19)])
mats  <- c(1,3,6,9,12,15,18,21,24,30,36,48,60,72,84,96,108,120)/12

## the obligatory perspective plot
persp(x = mat[,1], y = mats,mat[,-1],
      phi = 40, theta = 20, ticktype = "detailed",
      xlab = "time",
      ylab = "time to maturity in years",
      zlab = "zero rates in %")