NMOF (version 0.20-0)

NSf: Factor Loadings for Nelson--Siegel and Nelson--Siegel--Svensson

Description

Computes the factor loadings for Nelson--Siegel (NS) and Nelson--Siegel--Svensson (NSS) model for given lambda values.

Usage

NSf(lambda, tm)
NSSf(lambda1, lambda2, tm)

Arguments

lambda

the $\lambda$ parameter of the NS model (a scalar)

lambda1

the $\lambda_1$ parameter of the NSS model (a scalar)

lambda2

the $\lambda_2$ parameter of the NSS model (a scalar)

tm

a numeric vector with times-to-payment/maturity

Value

• For NS, a matrix with length(tm) rows and three columns. For NSS, a matrix with length(tm) rows and four columns.

Details

The function computes the factor loadings for given $\lambda$ parameters. Checking the correlation between these factor loadings can help to set reasonable $\lambda$ values for the NS/NSS models.

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

NS, NSS

Examples

## Nelson-Siegel
cor(NSf(lambda = 6, tm = 1:10)[-1L, -1L])

## Nelson-Siegel-Svensson
cor(NSSf(lambda1 = 1, lambda2 = 5, tm = 1:10)[-1L, -1L])
cor(NSSf(lambda1 = 4, lambda2 = 9, tm = 1:10)[-1L, -1L])