QuantLib：BondFunctions.zSpread 與“準確”價格不匹配

我正在使用 QuantLib 計算不同情況下固定利率債券的價格。第一步，我想通過使用 zspread 調整收益率曲線來複製目前市場價格。使用函式 BondFunctions.zSpread 我接近了（在下面的範例中（97.85 與 98 的市場價格），但我想知道為什麼在不斷改變點差時我們不會收斂到完全相同的價格。我錯過了什麼嗎？

下面的程式碼改編了Simple QuantLib Bond Math

import pytest
import QuantLib as ql

from QuantLib import *

# Construct yield curve
calc_date = Date(1, 1, 2017)
Settings.instance().evaluationDate = calc_date

spot_dates = [Date(1,1,2017), Date(1,1,2018), Date(1,1,2027)]
# corrected!
# spot_rates = [0.0, 0.04, 0.04]
spot_rates = [0.04, 0.04, 0.04]

day_count = SimpleDayCounter()
calendar = NullCalendar()
interpolation = Linear()
compounding = Compounded
# corrected!
compounding_frequency = Annual
compounding_frequency = Semiannual
spot_curve = ZeroCurve(spot_dates, spot_rates, day_count, calendar,
                      interpolation, compounding,
                      compounding_frequency)

spot_curve_handle = YieldTermStructureHandle(spot_curve)

# Construct bond schedule
issue_date = Date(1, 1, 2017)
maturity_date = Date(1, 1, 2022)
tenor = Period(Semiannual)
calendar = NullCalendar()
business_convention = Unadjusted
date_generation = DateGeneration.Backward
month_end = False

schedule = Schedule(issue_date, maturity_date, tenor, calendar,
                   business_convention, business_convention,
                   date_generation, month_end)

# Create FixedRateBond Object

coupon_rate = 0.05
coupons = [coupon_rate]
settlement_days = 0
face_value = 100

fixed_rate_bond = FixedRateBond(settlement_days,
                           face_value,
                           schedule,
                           coupons,
                           day_count)

# Set Valuation engine
bond_engine = DiscountingBondEngine(spot_curve_handle)
fixed_rate_bond.setPricingEngine(bond_engine)

# Calculate present value
value = fixed_rate_bond.NPV()
assert value == pytest.approx(104.49, abs=1.e-2)


# fix a hypothetical market price
px = 98.

# compute the implied z spread
zspread = ql.BondFunctions.zSpread(fixed_rate_bond,
                                  px,
                                  spot_curve, day_count, compounding,
                                  compounding_frequency, calc_date, 1.e-16, 1000000, 0.)


def impl_clean_price(spread):
   spread1 = ql.SimpleQuote(spread)
   spread_handle1 = ql.QuoteHandle(spread1)
   ts_spreaded1 = ql.ZeroSpreadedTermStructure(spot_curve_handle,
                                               spread_handle1)
   ts_spreaded_handle1 = ql.YieldTermStructureHandle(ts_spreaded1)
   ycsin = ts_spreaded_handle1
   fixed_rate_bond = FixedRateBond(settlement_days,
                                   face_value,
                                   schedule,
                                   coupons,
                                   day_count)
   # Set Valuation engine
   bond_engine = DiscountingBondEngine(ycsin)
   fixed_rate_bond.setPricingEngine(bond_engine)
   value = fixed_rate_bond.cleanPrice()
   return value

# the two clean prices are 98 and 97.8517891975
print px
print impl_clean_price(zspread)
print abs(px-impl_clean_price(zspread))

如果您沒有ZeroSpreadedTermStructure明確提供複利約定，它會將傳遞的價差視為連續複利，並相應地將其應用於基礎曲線。

您需要將曲線實例化為：

   ts_spreaded1 = ql.ZeroSpreadedTermStructure(spot_curve_handle,
                                               spread_handle1,
                                               compounding,
                                               compounding_frequency)

這將告訴ZeroSpreadedTermStructure如何解釋價差報價並得出正確的債券價格。

引用自：https://quant.stackexchange.com/questions/42710