nelson_siegel_svensson package

Submodules

nelson_siegel_svensson.calibrate module

Calibration methods for Nelson-Siegel(-Svensson) Models. See calibrate_ns_ols and calibrate_nss_ols for ordinary least squares (OLS) based methods.

nelson_siegel_svensson.calibrate.betas_ns_ols(tau: float, t: numpy.ndarray, y: numpy.ndarray) → Tuple[nelson_siegel_svensson.ns.NelsonSiegelCurve, Any]

Calculate the best-fitting beta-values given tau for time-value pairs t and y and return a corresponding Nelson-Siegel curve instance.

nelson_siegel_svensson.calibrate.betas_nss_ols(tau: Tuple[float, float], t: numpy.ndarray, y: numpy.ndarray) → Tuple[nelson_siegel_svensson.nss.NelsonSiegelSvenssonCurve, Any]

Calculate the best-fitting beta-values given tau (= array of tau1 and tau2) for time-value pairs t and y and return a corresponding Nelson-Siegel-Svensson curve instance.

nelson_siegel_svensson.calibrate.calibrate_ns_ols(t: numpy.ndarray, y: numpy.ndarray, tau0: float = 2.0) → Tuple[nelson_siegel_svensson.ns.NelsonSiegelCurve, Any]

Calibrate a Nelson-Siegel curve to time-value pairs t and y, by optimizing tau and chosing all betas using ordinary least squares.

nelson_siegel_svensson.calibrate.calibrate_nss_ols(t: numpy.ndarray, y: numpy.ndarray, tau0: Tuple[float, float] = (2.0, 5.0)) → Tuple[nelson_siegel_svensson.nss.NelsonSiegelSvenssonCurve, Any]

Calibrate a Nelson-Siegel-Svensson curve to time-value pairs t and y, by optimizing tau1 and tau2 and chosing all betas using ordinary least squares. This method does not work well regarding the recovery of true parameters.

nelson_siegel_svensson.calibrate.empirical_factors(y_3m: float, y_2y: float, y_10y: float) → Tuple[float, float, float]

Calculate the empirical factors according to Diebold and Li (2006).

nelson_siegel_svensson.calibrate.errorfn_ns_ols(tau: float, t: numpy.ndarray, y: numpy.ndarray) → float

Sum of squares error function for a Nelson-Siegel model and time-value pairs t and y. All betas are obtained by ordinary least squares given tau.

nelson_siegel_svensson.calibrate.errorfn_nss_ols(tau: Tuple[float, float], t: numpy.ndarray, y: numpy.ndarray) → float

Sum of squares error function for a Nelson-Siegel-Svensson model and time-value pairs t and y. All betas are obtained by ordinary least squares given tau (= array of tau1 and tau2).

nelson_siegel_svensson.cli module

Console script for nelson_siegel_svensson.

class nelson_siegel_svensson.cli.Curve

Bases: click.types.ParamType

Parameter type representing a curve (either Nelson-Siegel or Nelson-Siegel-Svensson)

convert(value, param, ctx)

Convert the value to the correct type. This is not called if the value is None (the missing value).

This must accept string values from the command line, as well as values that are already the correct type. It may also convert other compatible types.

The param and ctx arguments may be None in certain situations, such as when converting prompt input.

If the value cannot be converted, call fail() with a descriptive message.

Parameters:

• value – The value to convert.
• param – The parameter that is using this type to convert its value. May be None.
• ctx – The current context that arrived at this value. May be None.

name = 'curve'

class nelson_siegel_svensson.cli.FloatArray

Bases: click.types.ParamType

Parameter type representing an array of floats

convert(value, param, ctx)

Convert the value to the correct type. This is not called if the value is None (the missing value).

This must accept string values from the command line, as well as values that are already the correct type. It may also convert other compatible types.

The param and ctx arguments may be None in certain situations, such as when converting prompt input.

If the value cannot be converted, call fail() with a descriptive message.

Parameters:

• value – The value to convert.
• param – The parameter that is using this type to convert its value. May be None.
• ctx – The current context that arrived at this value. May be None.

name = 'floats'

nelson_siegel_svensson.ns module

Implementation of a Nelson-Siegel interest rate curve model. See NelsonSiegelCurve class for details.

class nelson_siegel_svensson.ns.NelsonSiegelCurve(beta0: float, beta1: float, beta2: float, tau: float)

Bases: object

Implementation of a Nelson-Siegel interest rate curve model. This curve can be interpreted as a factor model with three factors (including a constant).

factor_matrix(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Factor loadings for time(s) T as matrix columns, including constant column (=1.0).

factors(T: Union[float, numpy.ndarray]) → Union[Tuple[float, float], Tuple[numpy.ndarray, numpy.ndarray]]

Factor loadings for time(s) T, excluding constant.

forward(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Instantaneous forward rate(s) of this curve at time(s) T.

zero(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Zero rate(s) of this curve at time(s) T.

nelson_siegel_svensson.nss module

Implementation of a Nelson-Siegel-Svensson interest rate curve model. See NelsonSiegelSvenssonCurve class for details.

class nelson_siegel_svensson.nss.NelsonSiegelSvenssonCurve(beta0: float, beta1: float, beta2: float, beta3: float, tau1: float, tau2: float)

Bases: object

Implementation of a Nelson-Siegel-Svensson interest rate curve model. This curve can be interpreted as a factor model with four factors (including a constant).

factor_matrix(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Factor loadings for time(s) T as matrix columns, including constant column (=1.0).

factors(T: Union[float, numpy.ndarray]) → Union[Tuple[float, float, float], Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]]

Factor loadings for time(s) T, excluding constant.

forward(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Instantaneous forward rate(s) of this curve at time(s) T.

zero(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Zero rate(s) of this curve at time(s) T.

Module contents

Implementation of the Nelson-Siegel-Svensson interest rate curve model. For details, see classes NelsonSiegelCurve and NelsonSiegelSvenssonCurve.

class nelson_siegel_svensson.NelsonSiegelCurve(beta0: float, beta1: float, beta2: float, tau: float)

Bases: object

Implementation of a Nelson-Siegel interest rate curve model. This curve can be interpreted as a factor model with three factors (including a constant).

factor_matrix(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Factor loadings for time(s) T as matrix columns, including constant column (=1.0).

factors(T: Union[float, numpy.ndarray]) → Union[Tuple[float, float], Tuple[numpy.ndarray, numpy.ndarray]]

Factor loadings for time(s) T, excluding constant.

forward(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Instantaneous forward rate(s) of this curve at time(s) T.

zero(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Zero rate(s) of this curve at time(s) T.

class nelson_siegel_svensson.NelsonSiegelSvenssonCurve(beta0: float, beta1: float, beta2: float, beta3: float, tau1: float, tau2: float)

Bases: object

Implementation of a Nelson-Siegel-Svensson interest rate curve model. This curve can be interpreted as a factor model with four factors (including a constant).

factor_matrix(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Factor loadings for time(s) T as matrix columns, including constant column (=1.0).

factors(T: Union[float, numpy.ndarray]) → Union[Tuple[float, float, float], Tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]]

Factor loadings for time(s) T, excluding constant.

forward(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Instantaneous forward rate(s) of this curve at time(s) T.

zero(T: Union[float, numpy.ndarray]) → Union[float, numpy.ndarray]

Zero rate(s) of this curve at time(s) T.