QuantLib零息债券YTM、零利率与交割日处理：曲线构建与定价实践

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

# 日历和日计数约定
calendar = ql.NullCalendar() # 使用NullCalendar简化，实际应用中应使用对应市场日历
day_count = ql.Actual365Fixed()

# 面值
faceAmount = 100

# 债券数据：(发行日期, 到期日期, 票息率, 价格, 交割天数)
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_val, settlement_days in data:
    price_handle = ql.QuoteHandle(ql.SimpleQuote(price_val))

    # 注意：这里issue_date和maturity应基于字符串解析，而不是重新使用today
    issue_date = ql.Date(issue_date_str, '%d-%m-%Y')
    maturity = ql.Date(maturity_str, '%d-%m-%Y')

    # 附息债券的付息频率通常是半年，零息债券虽然没有票息，但仍需定义一个时间表
    # schedule的start_date通常是发行日或最近的付息日，但对于helper，有时可以简化
    # 这里为了与原始代码保持一致，使用today作为schedule的start_date
    schedule = ql.Schedule(today, maturity, ql.Period(ql.Semiannual), calendar, 
                           ql.DateGeneration.Backward, ql.Following, 
                           ql.DateGeneration.Backward, False)

    helper = ql.FixedRateBondHelper(price_handle, settlement_days, faceAmount, schedule, 
                                    [coupon / 100], day_count, False)
    helpers.append(helper)

# 构建收益率曲线
curve = ql.PiecewiseCubicZero(today, helpers, day_count)
curve.enableExtrapolation() # 启用外推

print("收益率曲线构建完成，并启用外推。")

# 示例：计算指定日期（例如第一个零息债券的到期日）的零利率、远期利率和折现因子
target_date = ql.Date(11, ql.December, 2023) # 对应第一个零息债券的到期日
zero_rate_eval_date = curve.zeroRate(target_date, day_count, ql.Annual, ql.Compounded).rate()
forward_rate_example = curve.forwardRate(today, target_date, day_count, ql.Annual, ql.Compounded).rate()
discount_factor_example = curve.discount(target_date)

print(f"\n评估日({today})到 {target_date} 的零利率: {zero_rate_eval_date*100:.4f}%")
print(f"评估日({today})到 {target_date} 的远期利率: {forward_rate_example*100:.4f}%")
print(f"评估日({today})到 {target_date} 的折现因子: {discount_factor_example:.4f}")

# 打印曲线节点上的零利率、远期利率和折现因子
node_data = {'Date': [], 'Zero Rates (Annual Compounded)': [], 
             'Forward Rates (Annual Compounded)': [], 'Discount Factors': []}

for dt in curve.dates():
    node_data['Date'].append(dt)
    # 修正：zeroRate和forwardRate应指定Compounded频率
    node_data['Zero Rates (Annual Compounded)'].append(curve.zeroRate(dt, day_count, ql.Annual, ql.Compounded).rate())
    node_data['Forward Rates (Annual Compounded)'].append(curve.forwardRate(dt, dt + ql.Period(1, ql.Years), day_count, ql.Annual, ql.Compounded).rate())
    node_data['Discount Factors'].append(curve.discount(dt))

node_dataframe = pd.DataFrame(node_data)
print("\n收益率曲线节点数据:")
print(node_dataframe)
# node_dataframe.to_excel('NodeRates.xlsx') # 可选：导出到Excel

# 创建一个DataFrame来存储债券结果
bond_results = {
    'Issue Date': [], 'Maturity Date': [], 'Coupon Rate': [], 'Price': [],
    'Settlement Days': [], 'Yield (from Settlement Date)': [], 
    'Zero Rate (from Evaluation Date)': [], 'Zero Rate (from Settlement Date)': [],
    'Discount Factor': [], 'Clean Price': [], 'Dirty Price': []
}

# 计算债券价格和收益率
for issue_date_str, maturity_str, coupon, price_val, settlement_days in data:
    price_handle = ql.QuoteHandle(ql.SimpleQuote(price_val))

    issue_date = ql.Date(issue_date_str, '%d-%m-%Y')
    maturity = ql.Date(maturity_str, '%d-%m-%Y')

    schedule = ql.Schedule(today, maturity, ql.Period(ql.Semiannual), calendar, 
                           ql.DateGeneration.Backward, ql.Following, 
                           ql.DateGeneration.Backward, False)

    # 使用构建好的收益率曲线设置定价引擎
    bondEngine = ql.DiscountingBondEngine(ql.YieldTermStructureHandle(curve))

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

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

    # 从评估日到期日的零利率
    zero_rate_eval_date = curve.zeroRate(maturity, day_count, ql.Annual, ql.Compounded).rate()

    # 从交割日到期日的零利率（应与零息债券的YTM匹配）
    # 对于附息债券，这个概念略有不同，但对于零息债券，它就是其YTM
    zero_rate_settlement_date = curve.forwardRate(bond.settlementDate(), maturity,
                                                  day_count, ql.Compounded, ql.Annual).rate()

    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 (from Settlement Date)'].append(bondYield)
    bond_results['Zero Rate (from Evaluation Date)'].append(zero_rate_eval_date)
    bond_results['Zero Rate (from Settlement Date)'].append(zero_rate_settlement_date) # 添加此项以展示校正
    bond_results['Discount Factor'].append(discount_factor)
    bond_results['Clean Price'].append(bondCleanPrice)
    bond_results['Dirty Price'].append(bondDirtyPrice)

# 从债券结果创建DataFrame
bond_results_df = pd.DataFrame(bond_results)

# 打印结果
print("\n债券定价与分析结果:")
print(bond_results_df)

# bond_results_df.to_excel('BondResults.xlsx') # 可选：导出到Excel