import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.interpolate import interp1d, CubicSpline
from scipy.optimize import curve_fit
plt.style.use('seaborn-v0_8')

deposits = pd.DataFrame({
    'Tenor':[7/365,1/12,0.25],
    'Rate':[0.018,0.019,0.021]
})
swaps = pd.DataFrame({
    'Tenor':[1,2,3],
    'SwapRate':[0.024,0.0265,0.029]
})
ois_quotes = pd.DataFrame({
    'Tenor':[0.5,1,2],
    'Rate':[0.019,0.020,0.021]
})
govbond = pd.DataFrame({
    "Instrument":["GovBond 5Y"],
    "Tenor":[5.0],
    "Rate":[0.025],
    "Category":["GovBond"]
})
deposits, swaps, ois_quotes, govbond

(      Tenor   Rate
 0  0.019178  0.018
 1  0.083333  0.019
 2  0.250000  0.021,
    Tenor  SwapRate
 0      1    0.0240
 1      2    0.0265
 2      3    0.0290,
    Tenor   Rate
 0    0.5  0.019
 1    1.0  0.020
 2    2.0  0.021,
    Instrument  Tenor   Rate Category
 0  GovBond 5Y    5.0  0.025  GovBond)

deposits_df = deposits.copy()
deposits_df["Instrument"] = ["Deposit 7D","Deposit 1M","Shibor 3M"]
deposits_df["Category"] = ["Deposit","Deposit","Shibor"]

swaps_df = swaps.rename(columns={"SwapRate":"Rate"})
swaps_df["Instrument"] = ["IRS 1Y","IRS 2Y","IRS 3Y"]
swaps_df["Category"] = "IRS"

ois_df = ois_quotes.copy()
ois_df["Instrument"] = ["OIS 6M","OIS 1Y","OIS 2Y"]
ois_df["Category"] = "OIS"

govbond_df = govbond.copy()
govbond_df["Instrument"] ="GovBond 5Y",
govbond_df["Category"] = "GovBond"

# govbond_df = pd.DataFrame({
#     "Instrument":["GovBond 5Y"],
#     "Tenor":[5.0],
#     "Rate":[0.025],
#     "Category":["GovBond"]
# })

# 合并
market = pd.concat([deposits_df, ois_df, swaps_df, govbond_df], ignore_index=True)
market

# 正确显示中文字符
import matplotlib
matplotlib.rcParams['font.sans-serif'] = ['SimHei']      # 使用黑体（SimHei）显示中文
matplotlib.rcParams['axes.unicode_minus'] = False        # 解决负号“‑”显示为方块问题
plt.figure(figsize=(7,4))
for cat,grp in market.groupby('Category'):
    plt.scatter(grp['Tenor'], grp['Rate'], label=cat)
plt.legend();plt.xlabel('期限(年)');plt.ylabel('年化利率(%)');plt.title('中国市场主要利率数据（示例）');

# Step1: 短端贴现因子
deposits['DF'] = 1 / (1 + deposits['Rate'] * deposits['Tenor'])
P = dict(zip(deposits['Tenor'], deposits['DF']))
P

{0.019178082191780823: 0.999654913646248,
 0.08333333333333333: 0.9984191696480573,
 0.25: 0.9947774185525988}

# Step2: 逐步自举 IRS 合约贴现因子
def bootstrap_swaps(P, swaps, alpha=0.25):
    for _, row in swaps.iterrows():
        K, Tn = row['SwapRate'], row['Tenor']
        N = int(Tn / alpha)
        known = sum(alpha * P[t] for t in P if t < Tn)
        P[Tn] = (1 - K * known) / (1 + K * alpha)
    return P

P = bootstrap_swaps(P, swaps)
sorted(P.items())

[(0.019178082191780823, 0.999654913646248),
 (0.08333333333333333, 0.9984191696480573),
 (0.25, 0.9947774185525988),
 (1.0, 0.9761857763309331),
 (2.0, 0.9672967868193934),
 (3.0, 0.9572713606639565)]

# Step3: 即期利率计算与绘图
T = np.array(sorted(P.keys()))
R = -np.log(np.array(list(P.values())))/T
# R = -np.log(np.array([P[t] for t in T])) / T
plt.plot(T, R*100, 'o-', label='Shibor 单曲线')
plt.xlabel('期限年'); plt.ylabel('即期利率(%)'); plt.legend(); plt.grid(True)
plt.title('单曲线自举结果'); plt.show()

# OIS贴现曲线
P_ois = {T:1/(1+R*T) for T,R in zip(ois_quotes['Tenor'], ois_quotes['Rate'])}
P_ois

{0.5: 0.9905894006934125, 1.0: 0.9803921568627451, 2.0: 0.9596928982725528}

# Shibor预测曲线 (简化迭代法)
alpha = 0.25
P_d = P_ois.copy()
for T,K in zip(swaps['Tenor'], swaps['SwapRate']):
    N = int(T/alpha)
    known = sum(alpha*P_d.get(round(i*alpha,2),1) for i in range(1,N))
    P_d[T] = (1 - K*known)/(1+K*alpha)

T_nodes = np.array(sorted(P_d.keys()))
L = (1/np.array(list(P_d.values())) - 1)/T_nodes
plt.plot(T_nodes, L*100, 's--', label='Shibor预测曲线')
plt.plot(ois_quotes['Tenor'], ois_quotes['Rate']*100, 'o-', label='OIS贴现曲线')
plt.xlabel('期限(年)'); plt.ylabel('利率(%)'); plt.legend(); plt.title('多曲线结构对比'); plt.show()

# 数据
T2 = np.array([0.25, 0.5, 1, 2, 3, 5])
R2 = np.array([0.021, 0.022, 0.024, 0.0265, 0.029, 0.025])

# lnP插值
lnP = -R2*T2
f_lnP = interp1d(T2, lnP, kind='linear', fill_value='extrapolate')

# Cubic Spline
cs = CubicSpline(T2, R2, bc_type='natural')

# 绘制对比
grid = np.linspace(0.1,5,100)
plt.plot(T2, R2*100, 'o', label='样本点')
plt.plot(grid, -f_lnP(grid)/grid*100, '--', label='lnP线性')
plt.plot(grid, cs(grid)*100, '-', label='Cubic Spline')
plt.xlabel('期限(年)'); plt.ylabel('利率%'); plt.legend(); plt.title('无套利插值比较'); plt.show()

# NSS模型拟合
def NSS(t,b0,b1,b2,b3,tau1,tau2):
    term1=(1-np.exp(-t/tau1))/(t/tau1)
    term2=term1-np.exp(-t/tau1)
    term3=(1-np.exp(-t/tau2))/(t/tau2)-np.exp(-t/tau2)
    return b0+b1*term1+b2*term2+b3*term3

popt,_=curve_fit(NSS,T2,R2,p0=[0.02,-0.01,0.01,0.005,1,3])
popt

c:\Users\wukek\anaconda3\lib\site-packages\scipy\optimize\_minpack_py.py:1010: OptimizeWarning: Covariance of the parameters could not be estimated
  warnings.warn('Covariance of the parameters could not be estimated',

array([ -1.85263945,   1.87189641,   2.00836947,   3.60424422,
        17.92262821, 797.78081835])

# Smith–Wilson外推简化版
def smith_wilson(t,UEP=0.02,alpha=0.1):
    return UEP + (R2[-1]-UEP)*np.exp(-alpha*(t-T2[-1]))

grid_long = np.linspace(0.1,30,300)
plt.plot(T2, R2*100,'o',label='市场点')
plt.plot(grid_long, NSS(grid_long,*popt)*100,'--',label='NSS拟合')
plt.plot(grid_long, smith_wilson(grid_long)*100,':',label='Smith–Wilson外推')
plt.legend(); plt.xlabel('期限(年)'); plt.ylabel('利率%'); plt.title('参数化模型比较'); plt.show()

def check_arbitrage(P):
    T = np.array(sorted(P.keys()))
    DF = np.array([P[t] for t in T])
    fwd = np.diff(-np.log(DF))/np.diff(T)
    if np.any(fwd<0): print('⚠️ 检测到负远期，需修正！')
    else: print('✅ 无负远期，曲线平稳')

check_arbitrage(P)

✅ 无负远期，曲线平稳

import json, datetime
version={'date':str(datetime.date.today()),'DF':P}
with open(f'curve_{version["date"]}.json','w') as f: json.dump(version,f,indent=2)
print('曲线已保存为版本：',version['date'])

曲线已保存为版本： 2025-10-22

T = np.array(sorted(P.keys()))
R = -np.log(np.array(list(P.values())))/T

def bond_price(y, c=0.029, T=3, freq=1):
    y = float(np.squeeze(y))  # 强制标量
    times = np.arange(1/freq, T+1/freq, 1/freq)
    cf = np.repeat(c/freq, len(times)); cf[-1] += 1
    disc = np.exp(-y * times)
    return np.sum(cf * disc)

y0 = float(np.squeeze(R[T == 3]))
dy = 0.0001
P0 = bond_price(y0)
P1 = bond_price(y0 + dy)
DV01 = (P0 - P1) / dy
print(f"DV01 = {DV01:.4f} per 1bp")

DV01 = 3.0396 per 1bp

key_rates=[1,3]
def key_rate_shift(R,shift,k):
    R2=R.copy()
    if k in key_rates:
        i=np.where(T==k)[0][0]; R2[i]+=shift
    return R2

for k in key_rates:
    R_shift=key_rate_shift(R,0.0001,k)
    y3=R_shift[T==3][0]
    print(f'KeyRate({k}Y): ΔP = {(bond_price(y0)-bond_price(y3))/0.0001:.4f}')

KeyRate(1Y): ΔP = 0.0000
KeyRate(3Y): ΔP = 3.0396

参数	含义	影响
$\beta_0$	长期均衡水平	决定长期利率收敛值
$\beta_1$	坡度	控制短端斜率
$\beta_2$	中段曲率	调整中期峰值
$\beta_3$	次曲率	再现多波峰结构
$\tau_1, \tau_2$	时间尺度	控制拐点位置

模型	使用场景	目的
NSS	商业银行、固定收益投资、国债曲线	拟合市场数据（灵活形态）
Smith–Wilson	保险公司、监管贴现曲线	长期外推，收敛至 UFR

收益率曲线构建全流程（中国市场实例）¶

📦 1. 准备环境与数据¶

数据结构说明¶

🧩 2. 单曲线自举 (Shibor 3M)¶

🌊 3. 多曲线体系 (OIS 贴现 + Shibor 预测)¶

🔧 4. 插值与平滑 (Hagan–West / Cubic / ln P)¶

方法一：ln P 线性插值¶

💡 思想¶

🔑 关键公式¶

✅ 特点¶

方法二：Cubic Spline（三次样条插值）¶

💡 思想¶

⚠️ 风险¶

方法三：Hagan–West 无套利平滑¶

💡 思想核心¶

🧠 5. 参数化建模 (NSS 与 Smith–Wilson)¶

Nelson–Siegel (NS) 模型概念¶

💡思想¶

🧮 公式¶

📈 特性¶

Nelson–Siegel–Svensson (NSS) 模型¶

💡思想¶

🧮 公式¶

📊 解释维度¶

☑️ 优点¶

⚠️ 缺点¶

Smith–Wilson (SW) 模型¶

💡思想来源¶

🧮 核心方程¶

🔑 Wilson 核¶

📈 长期性质¶

⚙️ 实务应用¶

⚙️ 6. 无套利检测与版本保存¶

📈 7. DV01 与 Key-Rate 敏感度¶

Key-Rate 敏感度（示意）¶

✅ 总结¶

	Tenor	Rate	Instrument	Category
0	0.019178	0.0180	Deposit 7D	Deposit
1	0.083333	0.0190	Deposit 1M	Deposit
2	0.250000	0.0210	Shibor 3M	Shibor
3	0.500000	0.0190	OIS 6M	OIS
4	1.000000	0.0200	OIS 1Y	OIS
5	2.000000	0.0210	OIS 2Y	OIS
6	1.000000	0.0240	IRS 1Y	IRS
7	2.000000	0.0265	IRS 2Y	IRS
8	3.000000	0.0290	IRS 3Y	IRS
9	5.000000	0.0250	GovBond 5Y	GovBond

收益率曲线构建全流程（中国市场实例）¶

📦 1. 准备环境与数据¶

数据结构说明¶

🧩 2. 单曲线自举 (Shibor 3M)¶

🌊 3. 多曲线体系 (OIS 贴现 + Shibor 预测)¶

🔧 4. 插值与平滑 (Hagan–West / Cubic / ln P)¶

方法一：ln P 线性插值¶

💡 思想¶

🔑 关键公式¶

✅ 特点¶

方法二：Cubic Spline（三次样条插值）¶

💡 思想¶

⚠️ 风险¶

方法三：Hagan–West 无套利平滑¶

💡 思想核心¶

🧠 5. 参数化建模 (NSS 与 Smith–Wilson)¶

Nelson–Siegel (NS) 模型概念¶

💡思想¶

🧮 公式¶

📈 特性¶

Nelson–Siegel–Svensson (NSS) 模型¶

💡思想¶

🧮 公式¶

📊 解释维度¶

☑️ 优点¶

⚠️ 缺点¶

Smith–Wilson (SW) 模型¶

💡思想来源¶

🧮 核心方程¶

🔑 Wilson 核¶

📈 长期性质¶

⚙️ 实务应用¶

⚙️ 6. 无套利检测与版本保存¶

📈 7. DV01 与 Key-Rate 敏感度¶

Key-Rate 敏感度（示意）¶

✅ 总结¶

🔧 4. 插值与平滑 (Hagan–West / Cubic / ln P)¶

方法一：ln P 线性插值¶

方法二：Cubic Spline（三次样条插值）¶