cashflows in fixedcouponbond

[Brad-11]

Hi,

this might be a really dumb question...

I was poking around in FixedCouponBond (QL 3.10), and tried to print out the
cashflows that it generates, by inserting something like this into the end of
the constructor in fixedcouponbond.cpp:

for(int i=0; i< cashFlows_.size(); i++) {
  std::cout << "date: " << schedule[i] << ", amount: " <<
  (*cashFlows_[i]).amount() << std::endl;
}

It looks as if when the coupon dates need to be adjusted (because they don't
fall on a weekday), this affects the amount of the cashflows, like so:
(This is with UnitedStates::GovernmentBond, Act360, and an annual coupon of 5%):

date: December 15th, 2044, amount: 5
date: December 15th, 2045, amount: 5.02778
date: December 17th, 2046, amount: 4.98611
date: December 16th, 2047, amount: 4.98611
date: December 15th, 2048, amount: 5
date: December 15th, 2049, amount: 5

This seems to happen because in fixedratecoupon.hpp, amount() is
nominal()*rate_*accrualPeriod(), and accrualPeriod (calculated in coupon.hpp),
depends on the dates in the schedule, which are adjusted to always fall on
business days.

Now here is the (possibly stupid) question: I would have expected that although
the date might be adjusted, the actual amount paid is not (that's the impression
I got from reading standard textbooks), i.e. I would have expected "Dec 16,
2047, amount: 5", "Dec 17 2046, amount: 5" and so on.

I have no idea how things work in the real world, though.

Have I missed something fundamental here? Can someone enlighten me?

Thank you for your patience.

Brad

[Toyin Akin]

Hi,

Let's say that you are recieving the coupon (5%) and the unadjusted end date
of the coupon
lands on a Sunday. Well the financial institution that owes you the coupon
payment is not open
and thus you have to wait until the Monday.

However a day has gone by and a one day interest has been earned on your
Notional.
Well that interest is yours. If you are happy to recieve just the 5%, the
financial institution
has just made money.

Actually you'll probably find that the next period is then shorter (in days)
and thus you'll probably recieve less than 5%. In the long run, it all
cancels out.

Toy out.

>From: Brad <[hidden email]>
>To: [hidden email]
>Subject: [Quantlib-users] cashflows in fixedcouponbond
>Date: Wed, 23 Nov 2005 16:16:23 +0000 (UTC)
>
>Hi,
>
>this might be a really dumb question...
>
>I was poking around in FixedCouponBond (QL 3.10), and tried to print out
>the
>cashflows that it generates, by inserting something like this into the end
>of
>the constructor in fixedcouponbond.cpp:
>
>for(int i=0; i< cashFlows_.size(); i++) {
>   std::cout << "date: " << schedule[i] << ", amount: " <<
>   (*cashFlows_[i]).amount() << std::endl;
>}
>
>It looks as if when the coupon dates need to be adjusted (because they
>don't
>fall on a weekday), this affects the amount of the cashflows, like so:
>(This is with UnitedStates::GovernmentBond, Act360, and an annual coupon of
>5%):
>
>date: December 15th, 2044, amount: 5
>date: December 15th, 2045, amount: 5.02778
>date: December 17th, 2046, amount: 4.98611
>date: December 16th, 2047, amount: 4.98611
>date: December 15th, 2048, amount: 5
>date: December 15th, 2049, amount: 5
>
>This seems to happen because in fixedratecoupon.hpp, amount() is
>nominal()*rate_*accrualPeriod(), and accrualPeriod (calculated in
>coupon.hpp),
>depends on the dates in the schedule, which are adjusted to always fall on
>business days.
>
>Now here is the (possibly stupid) question: I would have expected that
>although
>the date might be adjusted, the actual amount paid is not (that's the
>impression
>I got from reading standard textbooks), i.e. I would have expected "Dec 16,
>2047, amount: 5", "Dec 17 2046, amount: 5" and so on.
>
>I have no idea how things work in the real world, though.
>
>Have I missed something fundamental here? Can someone enlighten me?
>
>Thank you for your patience.
>
>Brad
>
>
>
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[Luigi Ballabio]

On 11/23/2005 05:16:23 PM, Brad wrote:
> I was poking around in FixedCouponBond (QL 3.10), and tried to print
> out the cashflows that it generates.
>
> It looks as if when the coupon dates need to be adjusted this affects  
> the amount of the cashflows.
>
> Now here is the (possibly stupid) question: I would have expected  
> that although the date might be adjusted, the actual amount paid is  
> not (that's the impression I got from reading standard textbooks)

Don't trust everything you read in textbooks :)

The amounts are indeed calculated based on the adjusted accrual period.  
However, different day-count conventions can depend in a smaller or a  
larger way from the underlying period. For instance, if you choose  
actual/actual ISMA---which, I think, is the convention for US  
government bonds---you should get 5 for all periods.

Later,
        Luigi

----------------------------------------

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make it so simple that there are obviously no deficiencies. And the
other way is to make it so complicated that there are no obvious
deficiencies.
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