使用 QuantLib Python 計算收益率曲線票面利率

我想使用 QuantLib Python 來計算掉期曲線的票面利率。

以下程式碼是我到目前為止所做的：

from QuantLib import *

# global data
calendar = TARGET()
todaysDate = Date(6,November,2001);
Settings.instance().evaluationDate = todaysDate
settlementDate = Date(8,November,2001);

# market quotes
deposits = { (1,Weeks): 0.0382,
            (1,Months): 0.0372,
            (3,Months): 0.0363,
            (6,Months): 0.0353,
            (9,Months): 0.0348,
            (1,Years): 0.0345 }

swaps = { (2,Years): 0.037125,
         (3,Years): 0.0398,
         (5,Years): 0.0443,
         (10,Years): 0.05165,
         (15,Years): 0.055175 }

# convert them to Quote objects
for n,unit in deposits.keys():
   deposits[(n,unit)] = SimpleQuote(deposits[(n,unit)])
for n,unit in swaps.keys():
   swaps[(n,unit)] = SimpleQuote(swaps[(n,unit)])

# build rate helpers

dayCounter = Actual360()
settlementDays = 2
depositHelpers = [ DepositRateHelper(QuoteHandle(deposits[(n,unit)]),
                                    Period(n,unit), settlementDays,
                                    calendar, ModifiedFollowing,
                                    False, dayCounter)
                  for n, unit in [(1,Weeks),(1,Months),(3,Months),
                                  (6,Months),(9,Months),(1,Years)] ]

fixedLegFrequency = Annual
fixedLegTenor = Period(1,Years)
fixedLegAdjustment = Unadjusted
fixedLegDayCounter = Thirty360()
floatingLegFrequency = Semiannual
floatingLegTenor = Period(6,Months)
floatingLegAdjustment = ModifiedFollowing
swapHelpers = [ SwapRateHelper(QuoteHandle(swaps[(n,unit)]),
                              Period(n,unit), calendar,
                              fixedLegFrequency, fixedLegAdjustment,
                              fixedLegDayCounter, Euribor6M())
               for n, unit in swaps.keys() ]

# term structure handles

discountTermStructure = RelinkableYieldTermStructureHandle()
forecastTermStructure = RelinkableYieldTermStructureHandle()

# term-structure construction

helpers = depositHelpers + swapHelpers
depoSwapCurve = PiecewiseFlatForward(settlementDate, helpers, Actual360())

ref_date = depoSwapCurve.referenceDate()
yc_day_count = depoSwapCurve.dayCounter()
tenor = Period(10, Years)

# 10Y Swap 

nominal = 1000000
maturity = calendar.advance(settlementDate,10,Years)

fixedRate = 0.04

floatingLegFrequency = Semiannual
spread = 0.0
fixingDays = 2
index = Euribor6M(forecastTermStructure)
floatingLegDayCounter = index.dayCounter()

fixedSchedule = Schedule(settlementDate, maturity,
                        fixedLegTenor, calendar,
                        fixedLegAdjustment, fixedLegAdjustment,
                        DateGeneration.Forward, False)
floatingSchedule = Schedule(settlementDate, maturity,
                           floatingLegTenor, calendar,
                           floatingLegAdjustment, floatingLegAdjustment,
                           DateGeneration.Forward, False)

swap = VanillaSwap(VanillaSwap.Receiver, nominal,
                  fixedSchedule, fixedRate, fixedLegDayCounter,
                  floatingSchedule, index, spread,
                  floatingLegDayCounter)
swap.setPricingEngine(swapEngine)


discountTermStructure.linkTo(depoSwapCurve)
forecastTermStructure.linkTo(depoSwapCurve)


print('original instrument par rate:')
print(swaps[(10, Years)].value())
print
print('calculated swap par rate:')
print(swap.fairRate())
print
print('calculated yield curve par rate:')
print(depoSwapCurve.forwardRate(ref_date, calendar.advance(ref_date, tenor), yc_day_count, Compounded ).rate())

從上面的程式碼我們可以看到，它swap.fairRate()返回的掉期利率與用於構造收益率曲線對象的原始掉期利率非常相似。這就是我要的。但是，這種計算掉期票面利率的方法非常麻煩，因為我不僅要計算 10Y 的掉期票面利率，還要計算 11Y、12Y、13Y 等的掉期票面利率……這意味著我必須創建一個單獨的 VanillaSwap對象為 11Y、12Y、13Y 等…

我計算掉期票面利率的第二種方法是depoSwapCurve.forwardRate(...)。但是，從上面的程式碼中我們可以看到，forwardRate(...)函式返回的值與用於構造收益率曲線對象的原始掉期利率有很大的不同。

我forwardRate(...)是否正確使用該函式來計算票面利率？或者有沒有更好的方法來計算收益率曲線對象的票面利率？

不，您必須創建不同的交換。 forwardRate(start, end)從頭到尾返回利率，中間不支付息票（Compounding慣例意味著年利息是再投資，而不是還清）。

為了讓這個過程不那麼繁瑣，我建議你定義一個函式parRate來獲取 start 和 end 日期，創建相應的交換，並返回其公平率。一旦你有了它，呼叫它應該只比呼叫複雜一點forwardRate。

引用自：https://quant.stackexchange.com/questions/37197