# -*- coding: utf-8 -*-
"""Calibration methods for Nelson-Siegel(-Svensson) Models.
See `calibrate_ns_ols` and `calibrate_nss_ols` for ordinary least squares
(OLS) based methods.
"""
from typing import Tuple, Any
import numpy as np
from numpy.linalg import lstsq
from scipy.optimize import minimize
from .ns import NelsonSiegelCurve
from .nss import NelsonSiegelSvenssonCurve
def _assert_same_shape(t: np.ndarray, y: np.ndarray) -> None:
assert t.shape == y.shape, "Mismatching shapes of time and values"
[docs]def betas_ns_ols(
tau: float, t: np.ndarray, y: np.ndarray
) -> Tuple[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.
"""
_assert_same_shape(t, y)
curve = NelsonSiegelCurve(0, 0, 0, tau)
factors = curve.factor_matrix(t)
lstsq_res = lstsq(factors, y, rcond=None)
beta = lstsq_res[0]
return NelsonSiegelCurve(beta[0], beta[1], beta[2], tau), lstsq_res
[docs]def errorfn_ns_ols(tau: float, t: np.ndarray, y: np.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.
"""
_assert_same_shape(t, y)
curve, lstsq_res = betas_ns_ols(tau, t, y)
return np.sum((curve(t) - y) ** 2)
[docs]def calibrate_ns_ols(
t: np.ndarray, y: np.ndarray, tau0: float = 2.0
) -> Tuple[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.
"""
_assert_same_shape(t, y)
opt_res = minimize(errorfn_ns_ols, x0=tau0, args=(t, y))
curve, lstsq_res = betas_ns_ols(opt_res.x[0], t, y)
return curve, opt_res
[docs]def 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)."""
return y_10y, y_10y - y_3m, 2 * y_2y - y_3m - y_10y
[docs]def betas_nss_ols(
tau: Tuple[float, float], t: np.ndarray, y: np.ndarray
) -> Tuple[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.
"""
_assert_same_shape(t, y)
curve = NelsonSiegelSvenssonCurve(0, 0, 0, 0, tau[0], tau[1])
factors = curve.factor_matrix(t)
lstsq_res = lstsq(factors, y, rcond=None)
beta = lstsq_res[0]
return (
NelsonSiegelSvenssonCurve(beta[0], beta[1], beta[2], beta[3], tau[0], tau[1]),
lstsq_res,
)
[docs]def errorfn_nss_ols(tau: Tuple[float, float], t: np.ndarray, y: np.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).
"""
_assert_same_shape(t, y)
curve, lstsq_res = betas_nss_ols(tau, t, y)
return np.sum((curve(t) - y) ** 2)
[docs]def calibrate_nss_ols(
t: np.ndarray, y: np.ndarray, tau0: Tuple[float, float] = (2.0, 5.0)
) -> Tuple[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.
"""
_assert_same_shape(t, y)
opt_res = minimize(errorfn_nss_ols, x0=np.array(tau0), args=(t, y))
curve, lstsq_res = betas_nss_ols(opt_res.x, t, y)
return curve, opt_res
