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: $β_{1}$ , $β_{2}$ , $β_{3}$ , $λ$ . For NSS: a vector: $β_{1}$ , $β_{2}$ , $β_{3}$ , $β_{4}$ , $λ_{1}$ , $λ_{2}$ .

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.

Schumann, E. (2017) Financial Optimisation with R (NMOF Manual). http://enricoschumann.net/NMOF.htm#NMOFmanual

Svensson, L.E. (1994) Estimating and Interpreting Forward Interest Rates: Sweden 1992--1994. IMF Working Paper 94/114.

Examples

Run this code

# NOT RUN {
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")


# }
# NOT RUN {
## 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[ ,-1L],
      phi = 30, theta = 30, ticktype = "detailed",
      xlab = "time",
      ylab = "time to maturity in years",
      zlab = "zero rates in %")
# }

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