ns

Syntax

ns(maturity, yield, [method='nm'], [maxIter], [bounds], [initialGuess], [seed])

Arguments

maturity is a numeric vector with non-negative elements, indicating the maturity (in years) of a bond.

yield is a numeric vector of the same length as maturity, indicating the bond yield.

method (optional) is a string indicating the model used. It can be:

  • 'nm' (default): Nelder-Mead simplex algorithm.
  • 'bfgs': BFGS algorithm.
  • 'lbfgs': LBFGS algorithm.
  • 'slsqp': Sequential Least Squares Programming algorithm.
  • 'de': Differential Evolution algorithm.

maxIter (optional) is an integral scalar or vector indicating the maximum number of iterations for the optimization algorithm during the fitting process.

bounds (optional) is a numeric matrix in the shape of (N,2), where N is the number of parameters to be optimized. The two elements of each row defines the bounds (min, max) on that parameter. Note that bounds only takes effect when method is 'lbfgs', ‘slsqp’ or ‘de’.

initialGuess (optional) is a numeric vector indicating the initial guess for the parameters that optimize the function.

NS model: The vector contains 4 elements: initial guess of β0, β1, β2, λ, with the default value [0.01, 0.01, 0.01, 1.0].

NSS model: The vector contains 6 elements: initial guess of β0, β1, β2, β3, λ0, λ1, with the default value [0.01, 0.01, 0.01, 0.01, 1.0, 1.0].

seed (optional) is an integer indicating the random number seed used in the differential evolution algorithm to ensure the reproducibility of results. It only takes effect when method='de'. If not specified, a non-deterministic random number generator is used.

Details

Fit yield curve using NS (Nelson-Siegel) model.

Return value: A dictionary with the following keys:

  • modelName: The model used.
  • params: The fitted model parameters.
    • NS model: a vector of length 4, containing β0, β1, β2, λ.
    • NSS model: a vector of length 6, containing β0, β1, β2, β3, λ0, λ1.
  • fminResult: The optimization result.
    • 'nm' : See fmin.
    • 'bfgs': See fminBFGS.
    • 'lbfgs': See fminLBFGSB.
    • 'slsqp': See fminSLSQP.
    • 'de': See differentialEvolution.
  • predict: The prediction function of the model, which returns the predicted yield with this model. It can be called using model.predict(T) or predict(model, T), where T is the maturity in years.

Examples

Use the bfgs method to fit yield curve based on NS (Nelson-Siegel) model.

maturity = [1,2,3,4,5,8,10,15,20,25,30]
yield = [0.0039,0.0061,NULL,NULL,0.0166,NULL,0.0258,NULL,NULL,0.0332,NULL]
model = ns(maturity, yield, method='bfgs');
model;
/*Output
modelName->ns
params->[0.037907009765789,-0.032345632006991,-0.048221596538028,1.48711064869407]
fminResult->xopt->[0.037907009765789,-0.032345632006991,-0.048221596538028,1.48711064869407]
fopt->7.682740281926149E-8
gopt->[0.000007050477817,-0.000001557728067,8.217072418048589E-7,-7.435919702203364E-8]
iterations->29
Hinv->#0                  #1                    #2                   #3                   
------------------- --------------------- -------------------- ---------------------
1.046957491287936   -2.422265785994416    4.016547235964936    174.575362711334378  
-2.422265785994413  20.767722224747515    -55.516118469836506  -1160.911707217612729
4.016547235964929   -55.516118469836506   162.441840532431541  3127.297987855009978 
174.575362711334378 -1160.911707217613638 3127.297987855011797 72743.950482441126951

warnFlag->0
fcalls->165
gcalls->33

predict->nssPredict
*/

Use the nm method to fit yield curve based on NS (Nelson-Siegel) model.

model = ns(maturity, yield, method='nm');
model;
/*Output
modelName->ns
modelName->ns
params->[-0.017297505365068,0.016544815374471,0.142682692134247,14.720778706012911]
fminResult->xopt->[-0.017297505365068,0.016544815374471,0.142682692134247,14.720778706012911]
fopt->0.000001443427918
iterations->446
fcalls->740
warnFlag->0

predict->nssPredict
*/

Related Function: nss