How QuantLib Schedule Dates Determine Bond Coupon Accruals

# Questions on the Day count issue in Bond pricing


# Questions on the Day count issue in Bond pricing












I failed to understand how does `QuantLib` manage the day-count issue when determining the actual Coupon payment. Below is my Fixed Rate Bond -

```
import QuantLib as ql
import pandas as pd

todaysDate = ql.Date(1, 9, 2019)
ql.Settings.instance().evaluationDate = todaysDate

spotDates = [todaysDate, todaysDate + ql.Period("1y"), todaysDate + ql.Period("2y"), todaysDate + ql.Period("3y")]
spotRates = [0, 0.066682, 0.067199, 0.067502]

dayCount = ql.ActualActual()
calendar = ql.Canada()
interpolation = ql.Linear()
compounding = ql.Compounded
compoundingFrequency = ql.Continuous

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

issueDate = todaysDate
maturityDate = todaysDate + ql.Period("2y")
tenor = ql.Period(ql.Annual)
bussinessConvention = ql.Following
dateGeneration = ql.DateGeneration.Backward
monthEnd = False

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

couponRate = 0.09
coupons = [couponRate]

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

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

fixedRateBond.NPV()
```

Now, I want to see the actual CFs which `QuantLib` is considering

```
for cf in fixedRateBond.cashflows():
    print(cf.date().ISO(), cf.amount())
```

This gives -

```
2020-09-01 8.958904109589039
2021-09-01 8.991780821917805
2021-09-01 100.0
```

But my question is how the 1st 2 numbers are calculated. With `Actual-Actual` convention, shouldnt the 1st number would be :

```
>>> 9 * dayCount.yearFraction(issueDate + ql.Period("1d"),issueDate + ql.Period("1y"))
8.983561643835616
```

And for the 2nd Interest payment

```
>>> 9 * dayCount.yearFraction(issueDate + ql.Period("1y") + ql.Period("1d"),issueDate + ql.Period("2y"))
8.967190657983382
```

Can you please help me to understand the calculation - what am I missing here?

## Answer by David Duarte (score 1, accepted)

https://quant.stackexchange.com/a/57469

The date you are using as issueDate (01-09-2019) is a Sunday, and because you are using the Canadian Calendar, the 2nd of september is a holiday (Labor Day) so the first date would actually be 03-09-2019.

Check the dates of the schedule:

```
for dt in schedule:
    print(dt)
```

September 3rd, 2019 September 1st, 2020 September 1st, 2021

Notice that when building the schedule, some dates may be adjusted with the calendar and conventions, so if you want to check how the first coupon is being determined, you should actually use:

```
dayCount.yearFraction(schedule[0], schedule[1]) * couponRate * 100
```

which gives you:

8.95890410958904

Also, note that `Date + Period` is not a good idea because it will "blindly" add a period to a date and the result might not be a business day. Using `calendar.advance(Date, Period)` would be better