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)
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 |
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.
For NS, a matrix with length(tm) rows and three columns.
For NSS, a matrix with length(tm) rows and four columns.
Enrico Schumann
Gilli, M. and Grosse, S. and Schumann, E. (2010) Calibrating the Nelson-Siegel-Svensson model, COMISEF Working Paper Series No. 031. http://enricoschumann.net/COMISEF/wps031.pdf
Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. https://www.elsevier.com/books/numerical-methods-and-optimization-in-finance/gilli/978-0-12-815065-8
Gilli, M. and Schumann, E. (2010) A Note on ‘Good’ Starting Values in Numerical Optimisation, COMISEF Working Paper Series No. 044. http://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. (2019) 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.
## 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])
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