NSf function

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

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

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

Arguments

• lambda: the $lambda$ parameter of the NS model (a scalar)
• lambda1: the $lambda1$ parameter of the NSS model (a scalar)
• lambda2: the $lambda2$ parameter of the NSS model (a scalar)
• tm: a numeric vector with times-to-payment/maturity

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.

Returns

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

References

Gilli, M. and Grosse, S. and Schumann, E. (2010) Calibrating the Nelson-Siegel-Svensson model, COMISEF Working Paper Series No. 031. https://enricoschumann.net/COMISEF/wps031.pdf

Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. tools:::Rd_expr_doi("10.1016/C2017-0-01621-X")

Gilli, M. and Schumann, E. (2010) A Note on Good Starting Values in Numerical Optimisation, COMISEF Working Paper Series No. 044. https://enricoschumann.net/COMISEF/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. (2023) Financial Optimisation with R (NMOF Manual). https://enricoschumann.net/NMOF.htm#NMOFmanual

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

Author(s)

Enrico Schumann

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])