Fixed-Rate Bond Coupon Amounts and Day-Count Conventions in QuantLib

# Pricing a fixed rate bond in Quantlib Python


# Pricing a fixed rate bond in Quantlib Python












I'm trying to implement a pricing model for fixed rate bonds with the code below.

```
import QuantLib as ql
import pandas as pd

todaysDate = ql.Date(31, 8, 2017)
ql.Settings.instance().evaluationDate = todaysDate

spotDates = [ql.Date(1,9,2017), ql.Date(5,9,2017), ql.Date(7,9,2017), ql.Date(14,9,2017),   ql.Date(21,9,2017), ql.Date(2,10,2017), ql.Date(31,10,2017), ql.Date(30,11,2017), ql.Date(2,1,2018), ql.Date(31,1,2018), ql.Date(28,2,2018), ql.Date(3,4,2018), ql.Date(30,4,2018)]
spotRates = [0.066682, 0.067199, 0.067502, 0.068526, 0.069462, 0.070742, 0.072984, 0.073566, 0.073174, 0.072844, 0.072610, 0.072467, 0.072366]

dayCount = ql.Actual365Fixed()
calendar = ql.SouthAfrica()
interpolation = ql.Linear()
compounding = ql.Compounded
compoundingFrequency = ql.Semiannual

spotCurve = ql.ZeroCurve(spotDates, spotRates, dayCount, calendar, 
interpolation, compounding, compoundingFrequency)
spotCurveHandle = ql.YieldTermStructureHandle(spotCurve)

issueDate = ql.Date(20, 4, 2009)
maturityDate = ql.Date(20, 4, 2018)
tenor = ql.Period(ql.Semiannual)
calendar = ql.SouthAfrica()
bussinessConvention = ql.Following
dateGeneration = ql.DateGeneration.Backward
monthEnd = False

schedule = ql.Schedule (issueDate, maturityDate, tenor, calendar, bussinessConvention, bussinessConvention, dateGeneration, monthEnd)

dayCount = ql.Actual365Fixed()
couponRate = 0.0925
coupons = [couponRate]

settlementDays = 3
faceValue = 100
fixedRateBond = ql.FixedRateBond(settlementDays, faceValue, schedule, coupons, dayCount)

bondEngine = ql.DiscountingBondEngine(spotCurveHandle)
fixedRateBond.setPricingEngine(bondEngine)

fixedRateBond.NPV()
print(fixedRateBond.NPV())
print(fixedRateBond.dirtyPrice())
print(fixedRateBond.cleanPrice())
print(fixedRateBond.accruedAmount())
print(fixedRateBond.dayCounter())
print(fixedRateBond.settlementDate())

for c in fixedRateBond.cashflows():
    print('%20s %12f' % (c.date(), c.amount()))
```

My cash flow schedule looks a bit strange, I would have expected values of 4.625.

```
October 20th, 2009     4.637671
April 20th, 2010       4.612329
October 20th, 2010     4.637671
April 20th, 2011       4.612329
October 20th, 2011     4.637671
April 20th, 2012       4.637671
October 22nd, 2012     4.688356
April 22nd, 2013       4.612329
October 21st, 2013     4.612329
April 22nd, 2014       4.637671
October 20th, 2014     4.586986
April 20th, 2015       4.612329
October 20th, 2015     4.637671
April 20th, 2016       4.637671
October 20th, 2016     4.637671
April 20th, 2017       4.612329
October 20th, 2017     4.637671
April 20th, 2018       4.612329
April 20th, 2018     100.000000
```

Model values produced are:

```
104.60163528858176
104.6774279539175
101.18016767994489
3.497260273972613
Actual/365 (Fixed) day counter
September 5th, 2017
```

The value I get for accrued interest is spot on with the values provided by our internal system, but the prices are a bit off. Clean price expectation is 100.81517 and Dirty price expectation is 104.31243

## Answer by bn_ln (score 6)

https://quant.stackexchange.com/a/46108

try:

`dayCount = ql.ActualActual(ql.ActualActual.ISMA,schedule)`

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/46119

Your bond pays fixed 9.25% a year, twice a year. For most fixed-coupon bonds, the coupon is not "daycounted" - it should be exactly annual coupon / frequency = 4.625% (there are very few exceptions, like Mexican mbonos). The daycount is used if you need to calculate the accrued in the middle of the coupon period, e.g. to get a dirty price. For most fixed-coupon loans, lpns, fixed-copon legs of IR swaps, etc the market convention is to daycount the coupons, which is what your code does.

Just focusing on projecting the expected cash flows, I don't think changing the daycount convention to Actual / Actual would help. It would result in period fraction being 182/365 or 183/365 or (in leap year) /366, while you want exactly 1/2, irrespecive of holidays and number of days in various months. It would also produce different accrued during the coupon period, and you're satisfied with the accrued you have now.

I think (haven't tried) a way to get the desired cash flows from QL may be to change the bussinessConvention that you pass to the schedule from

bussinessConvention = ql.Following

to bussinessConvention = ql.Unadjusted

But then you do want the discount factors that you apply to your cash flows to be on business days (adjusted for weekends and holidays).

## Answer by Gustavo (score 0)

https://quant.stackexchange.com/a/54167

I've needed to do the exact same simple thing and found the solution to be to set both `daycount = SimpleDayCounter()` and `bussinessConvention = Unadjusted`