Swap Par Rates Versus Forward Rates from a Yield Curve

# Use QuantLib Python to calculate yield curve par rates


# Use QuantLib Python to calculate yield curve par rates












I would want to use QuantLib Python to calculate par rates of a swap curve.

The following code is what I've done so far:

```
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())
```

From the code above we can see that `swap.fairRate()` returns the par rate of the swap which is very similar to the original swap rate used to construct the yield curve object. This is what I want. However, this method of calculating swap par rate is quite cumbersome, because I want to calculate swap par rate not only for 10Y, but also for 11Y, 12Y, 13Y etc... This means that I'll have to create a separate VanillaSwap object for 11Y, 12Y, 13Y etc...

My second way to calculate swap par rate is `depoSwapCurve.forwardRate(...)`. However, from the code above we can see that the value returned by the `forwardRate(...)` function is quite different from the original swap rate used to construct the yield curve object.

Am I using the `forwardRate(...)` function correctly to calculate par rate? Or is there a better way to calculate par rate from a yield curve object?

## Answer by Luigi Ballabio (score 5, accepted)

https://quant.stackexchange.com/a/37252

No, you'll have to create different swaps. `forwardRate(start, end)` returns the rate from start to end without paying coupons in between (the `Compounding` convention means that the annual interest is reinvested, not paid off).

To make the process less cumbersome, I suggest you define a function `parRate` that takes the starlt and end dates, creates the corresponding swap, and returns its fair rate. Once you have it, calling it should be only slightly more complex than calling `forwardRate`.