# nelsonsiegelsvensson#

Functions

 `NSSGoodFit`(params, TimeVec, YieldVec) NSSGoodFit calculates the residuals between the yield predicted by the NSS algorithm with the specified parameterisation and the market observed ones. `NSSMinimize`(beta0, beta1, beta2, beta3, ...) NSSMinimize uses the built in minimize function from the python's scipy package. `NelsonSiegelSvensson`(T, beta0, beta1, beta2, ...) NelsonSiegelSvensson calculates the interpolated/extrapolated curve at points in the array "T" using the Nelson-Siegel-Svannson algorithm, parameterized with parameters beta0, beta1, beta2, beta3, lambda0, lambda1.
NelsonSiegelSvensson(T, beta0, beta1, beta2, beta3, lambda0, lambda1)[source]#

NelsonSiegelSvensson calculates the interpolated/extrapolated curve at points in the array “T” using the Nelson-Siegel-Svannson algorithm, parameterized with parameters beta0, beta1, beta2, beta3, lambda0, lambda1. It returns a numpy ndarray of points.

Parameters:
• T – n x 1 ndarray of maturities for which the user wants to calculate the coresponding rate

• beta0 – 1 x 1 floating number, representing the first factor of the NSS parametrisation

• beta1 – 1 x 1 floating number, representing the second factor of the NSS parametrisation

• beta2 – 1 x 1 floating number, representing the third factor of the NSS parametrisation

• beta3 – 1 x 1 floating number, representing the fourth factor of the NSS parametrisation

• lambda0 – 1 x 1 floating number, representing the first shape parameter lambda of the NSS parametrisation

• lambda1 – 1 x 1 floating number, representing the second shape parameter lambda of the NSS parametrisation

Returns:

n x 1 ndarray of interpolated/extrapolarted points coresponding to maturities inside T. Where n is the length of the vector T.

NSSGoodFit(params, TimeVec, YieldVec)[source]#

NSSGoodFit calculates the residuals between the yield predicted by the NSS algorithm with the specified parameterisation and the market observed ones.

Parameters:
• params – 6 x 1 tuple containing the 6 parameters of the NSS algorithm. The sequence of parameters needs to be (beta0, …, beta4, lambda0, lambda1)

• TimeVec – n x 1 ndarray of maturities for which the yields in YieldVec were observed

• YieldVec – n x 1 ndarray of observed yields

Returns:

1 x 1 float number Euclidian distance between the calculated points and observed data

NSSMinimize(beta0, beta1, beta2, beta3, lambda0, lambda1, TimeVec, YieldVec)[source]#

NSSMinimize uses the built in minimize function from the python’s scipy package. The function sets up the parameters and the function NSSGoodFit as to make it compatible with the way minimize requires its arguments. If the optimization does not converge, the output is an empty array.

Parameters:
• beta0 – 1 x 1 floating number, representing the first factor of the NSS parametrisation

• beta1 – 1 x 1 floating number, representing the second factor of the NSS parametrisation

• beta2 – 1 x 1 floating number, representing the third factor of the NSS parametrisation

• beta3 – 1 x 1 floating number, representing the fourth factor of the NSS parametrisation

• lambda0 – 1 x 1 floating number, representing the first shape parameter lambda of the NSS parametrisation

• lambda1 – 1 x 1 floating number, representing the second shape parameter lambda of the NSS parametrisation

• TimeVec – n x 1 ndarray of maturities for which the yields in YieldVec were observed

• YieldVec – n x 1 ndarray of observed yields

Returns:

6 x 1 array of parameters and factors, that best fit the observed yields(Or an empty array if the optimization was not successfull).