校准收益率曲线参数 Nelson Siegel Svensson

Question

[编辑] 亲爱的团队

，我与 Nelson Siegel Svensson 收益率曲线合作，我需要通过最小二乘法校准参数 b0、b1、b2、b3 和 tau0、tau1，与实际 X、Y 数据和使用收益率曲线估计的 Y 相关，我有以下代码搜索校准，但我不确定这是实现目标的最佳策略：

from scipy.optimize import least_squares
import numpy as np
from math import exp as EXP, trunc
from nelson_siegel_svensson import NelsonSiegelSvenssonCurve
import pandas as pd
import matplotlib.pyplot as plt

def model(x, const):
    arr = np.array([])
    for val in const:
        arr = np.append(arr,(x[0])+(x[1]*((1-EXP(-val/x[4]))/(val/x[4])))+(x[2]*((((1-EXP(-val/x[4]))/(val/x[4])))-(EXP(-val/x[4]))))+x[3]*((((1-EXP(-val/x[5]))/(val/x[5])))-(EXP(-val/x[5]))))
    return arr
 
def fun(x, const, y_real):
    return y_real - model(x,const)
 
 
# days
const = np.array([30,90,270,548,913,1278,1643,2008,2373,2738,3103,3468,3833,4198,4563,4928,5293,5658,6023,6388,6935,7300,7665,8030])/365

# empty values represented with 0
y_real = np.array([3.33156,3.44928,3.62778,3.74313,3.96015,4.384,4.4705,4.55701,4.63817,4.69949,4.76081,4.82213,4.87285,4.8681,4.86336,4.85861,4.85387,4.84912,4.87039,4.89833,4.94286,4.98739,5.03192,5.07645])

# initial coefficients of Nelson Siegel Svensson
x0 = np.array([0.0001, 0.0001, 0.0001, 0.0001, 1.0, 1.0])

res = least_squares(fun, x0, bounds=(0,5000), args=(const, y_real), verbose=1)
 
print(res.x)

X_fix = np.linspace(start=const[0], stop=const[-1], num=(const.size*20))

NSS = NelsonSiegelSvenssonCurve(beta0=res.x[0], beta1=res.x[1], beta2=res.x[2], beta3=res.x[3], tau1=res.x[4], tau2=res.x[5])

pd_interpolation = pd.DataFrame(columns=['Period','Value'])

font = {'family': 'serif',
    'color':  '#1F618D',
    'weight': 'bold',
    'size': 14,
    }

font_x_y = {'family': 'serif',
    'color':  '#C70039',
    'weight': 'bold',
    'size': 13,
    'style': 'oblique' 
    }

fig, ax = plt.subplots(nrows=1, ncols=1, figsize=(10, 6))

minx = -const[1]*3

config_manager = plt.get_current_fig_manager()
config_manager.set_window_title("Visualización " )

screen_x, screen_y = config_manager.window.wm_maxsize()

anchura = str(trunc(screen_x/12))
altura = str(trunc(screen_y/8))
middle_window = "+" + anchura + "+" + altura

config_manager.window.wm_geometry(middle_window)

plt.title('Interpolación ', fontdict=font, loc='center')
plt.xlabel('Periodo', fontdict=font_x_y)
plt.ylabel('Aproximación', fontdict=font_x_y, rotation=90, labelpad=10)

ax.set_ylim(ymin=0, ymax=(np.amax(y_real)*1.1))
ax.set_xlim(xmin=minx, xmax=(np.amax(const)*1.03))

ax.plot(const, y_real, 'ro', label='Dato real')
ax.plot(X_fix, NSS(X_fix),'--', label='Dato interpolado')
ax.legend(loc='lower right', frameon=False)

plt.show()

结果是：

您还有其他最佳选择吗？

提前致谢。