QuantLib Python实战：零息债券收益率、零利率与结算日折扣的精确处理

import pandas as pd
import matplotlib.pyplot as plt
import QuantLib as ql

# 设置评估日期
today = ql.Date(21, ql.November, 2023)
ql.Settings.instance().evaluationDate = today

# 定义日历和日计数约定
calendar = ql.NullCalendar() # 使用空日历，表示所有日期都是工作日
day_count = ql.Actual365Fixed() # 实际天数/365固定日计数

# 债券参数
faceAmount = 100 # 面值

# 债券数据：(发行日期, 到期日期, 票息率, 市场价格, 结算天数)
data = [
    ('11-09-2023', '11-12-2023', 0, 99.524, 4), # 零息债券
    ('11-09-2023', '11-03-2024', 0, 96.539, 4), # 零息债券
    ('11-09-2023', '10-06-2024', 0, 93.552, 4), # 零息债券
    ('11-09-2023', '09-09-2024', 0, 89.510, 4), # 零息债券
    ('22-08-2022', '22-08-2024', 9.0, 96.406933, 3), # 附息债券
    ('27-06-2022', '27-06-2025', 10.0, 88.567570, 3), # 附息债券
    ('27-06-2022', '27-06-2027', 11.0, 71.363073, 3), # 附息债券
    ('22-08-2022', '22-08-2029', 12.0, 62.911623, 3), # 附息债券
    ('27-06-2022', '27-06-2032', 13.0, 55.976845, 3), # 附息债券
    ('22-08-2022', '22-08-2037', 14.0, 52.656596, 3)  # 附息债券
]

helpers = []
for issue_date_str, maturity_str, coupon, price, settlement_days in data:
    price_handle = ql.QuoteHandle(ql.SimpleQuote(price))
    issue_date = ql.Date(issue_date_str, '%d-%m-%Y')
    maturity = ql.Date(maturity_str, '%d-%m-%Y')

    # 构建债券支付时间表
    # schedule的第一个参数通常是有效日期，此处使用today作为基准
    schedule = ql.Schedule(today, maturity, ql.Period(ql.Semiannual), calendar, 
                           ql.DateGeneration.Backward, ql.Following, 
                           ql.DateGeneration.Backward, False)

    # 创建债券辅助工具
    helper = ql.FixedRateBondHelper(price_handle, settlement_days, faceAmount, 
                                    schedule, [coupon / 100], day_count, False)
    helpers.append(helper)

# 引导零利率曲线
curve = ql.PiecewiseCubicZero(today, helpers, day_count)

# 启用外推，以便计算超出观测数据范围的利率
curve.enableExtrapolation()

print("收益率曲线已成功构建。")

# 创建一个空的DataFrame来存储结果
bond_results = {
    'Issue Date': [],
    'Maturity Date': [],
    'Coupon Rate': [],
    'Price': [],
    'Settlement Days': [],
    'Yield (YTM)': [],
    'Zero Rate (Settlement to Maturity)': [], # 修正后的零利率
    'Zero Rate (Evaluation to Maturity)': [], # 评估日到期日零利率
    'Discount Factor': [],
    'Clean Price': [],
    'Dirty Price': []
}

# 计算债券价格和收益率
for issue_date_str, maturity_str, coupon, price, settlement_days in data:
    price_handle = ql.QuoteHandle(ql.SimpleQuote(price))
    issue_date = ql.Date(issue_date_str, '%d-%m-%Y')
    maturity = ql.Date(maturity_str, '%d-%m-%Y')

    # 债券支付时间表 (与helper中使用的schedule保持一致)
    schedule = ql.Schedule(today, maturity, ql.Period(ql.Semiannual), calendar, 
                           ql.DateGeneration.Backward, ql.Following, 
                           ql.DateGeneration.Backward, False)

    # 创建债券对象
    bond = ql.FixedRateBond(settlement_days, faceAmount, schedule, 
                            [coupon / 100], day_count)

    # 设置定价引擎，使用已引导的收益率曲线
    bondEngine = ql.DiscountingBondEngine(ql.YieldTermStructureHandle(curve))
    bond.setPricingEngine(bondEngine)

    # 计算债券YTM、净价和全价
    bondYield = bond.bondYield(day_count, ql.Compounded, ql.Annual)
    bondCleanPrice = bond.cleanPrice()
    bondDirtyPrice = bond.dirtyPrice()

    # 修正后的零利率：从结算日期到到期日期的远期零利率
    # 对于零息债券，这应该与YTM非常接近
    zero_rate_settlement_to_maturity = curve.forwardRate(
        bond.settlementDate(), maturity, day_count, ql.Compounded, ql.Annual
    ).rate()

    # 从评估日期到到期日期的零利率 (用于比较)
    zero_rate_evaluation_to_maturity = curve.zeroRate(
        maturity, day_count, ql.Compounded, ql.Annual
    ).rate()

    # 从评估日期到到期日期的折现因子
    discount_factor = curve.discount(maturity)

    # 将结果添加到DataFrame
    bond_results['Issue Date'].append(issue_date)
    bond_results['Maturity Date'].append(maturity)
    bond_results['Coupon Rate'].append(coupon)
    bond_results['Price'].append(price_handle.value())
    bond_results['Settlement Days'].append(settlement_days)
    bond_results['Yield (YTM)'].append(bondYield)
    bond_results['Zero Rate (Settlement to Maturity)'].append(zero_rate_settlement_to_maturity)
    bond_results['Zero Rate (Evaluation to Maturity)'].append(zero_rate_evaluation_to_maturity)
    bond_results['Discount Factor'].append(discount_factor)
    bond_results['Clean Price'].append(bondCleanPrice)
    bond_results['Dirty Price'].append(bondDirtyPrice)

# 从结果创建DataFrame
bond_results_df = pd.DataFrame(bond_results)

# 打印结果
print("\n债券定价与收益率分析结果:")
print(bond_results_df)

# 输出到Excel
bond_results_df.to_excel('BondResults.xlsx', index=False)

# 打印曲线节点上的零利率、远期利率和折现因子
print("\n收益率曲线节点数据:")
node_data = {'Date': [],
             'Zero Rates (Evaluation to Date)': [],
             'Forward Rates (1Y)': [],
             'Discount Factors': []}

for dt in curve.dates():
    node_data['Date'].append(dt)
    node_data['Zero Rates (Evaluation to Date)'].append(
        curve.zeroRate(dt, day_count, ql.Compounded, ql.Annual).rate()
    )
    node_data['Forward Rates (1Y)'].append(
        curve.forwardRate(dt, dt + ql.Period(1, ql.Years), day_count, ql.Compounded, ql.Annual).rate()
    )
    node_data['Discount Factors'].append(curve.discount(dt))

node_dataframe = pd.DataFrame(node_data)
print(node_dataframe)
node_dataframe.to_excel('NodeRates.xlsx', index=False)