ParCoupon class

[Andre Louw-2]

Nicolas,

Can you explain to me the difference between a Par Coupon and an Indexed
Coupon?

André Louw
Decillion Limited - "Your Risk Is Our Domain"

Email: [hidden email]
Office: [phone]
Mobile: [phone]
Fax: [phone]

 
-------------------------------------------------------------------------
This e-mail is intended only for the use of the individual or entity named
above and may contain information that is confidential and privileged,
proprietary to the company and protected by law. If you are not the intended
recipient, you are hereby notified that any dissemination, distribution or
copying of this e-mail is strictly prohibited. Opinions, conclusions and
other information in this message that do not relate to the official
business of our company shall be understood as neither given nor endorsed by
it.

[Luigi Ballabio-2]

At 02:58 PM 4/30/03 +0200, Andre Louw wrote:
>Can you explain to me the difference between a Par Coupon and an Indexed
>Coupon?

Andre,
         due to holidays and rolling conventions, the end date of a coupon
starting at a given date might not match the end date of the corresponding
Euribor deposit starting at the same date. Example: take a 5-year sequence
of semi-annual coupons starting May 5, 2003 on the TARGET calendar. Their
start/end dates are:

May 5th, 2003
November 5th, 2003
May 5th, 2004
November 5th, 2004
May 5th, 2005
November 7th, 2005
May 5th, 2006
November 6th, 2006
May 7th, 2007
November 5th, 2007
May 5th, 2008

so that, for instance, the penultimate coupon starts May 7, 2007 and ends
November 5th, 2007. But the 6-months Euribor fixing of May 7, 2007 is based
on a deposit with end date November 7th, 2007!
ParCoupon and IndexedCoupon are two different approaches to this date
mismatch, namely:

let's call "start" the start date, "end_1" the end date of the coupon, and
"end_2" the end date of the deposit underlying the Euribor fixing.

1) ParCoupon calculates the coupon rate as
         rate = (discount(end_1)/discount(start) - 1)/T
    where T is the period between start and end_1. This has the advantage
    that the NPV of a bond nicely adds up to 100 when the redemption is
    included, and that each rate is paid for the exact period over which
    it is calculated---i.e., no convexity. However, when May 7th, 2007 comes,
    the coupon will fix based on the underlying deposit dates!

2) IndexedCoupon forecasts the coupon rate based on the deposit, i.e. as:
         rate = (discount(end_2)/discount(start) - 1)/T
    where T is the period between start and end_2. This is the rate as will
    be fixed when May 7th, 2007 comes. However, it will be accrued over a
    different period, namely, between start and end_1, which introduces a
    small convexity error.

Therefore, IndexedCoupon accrues wrongly the right fixing, while ParCoupon
accrues rightly the wrong fixing. As I never sat down to try and estimate
which error is smaller, I'm not suggesting that either is best...

Bye,
         Luigi

[Andre Louw-2]

Thanx Luigi,

One more thing, in the inheritance tree, IndexedCoupon has both InArrear,
and UpFront Coupons inheriting from it. ParCoupon has nothing, is this
portion still missing or am I missing something? Is it not possible to have
a "par" coupon fixing at the end?

Andre

 
-------------------------------------------------------------------------
This e-mail is intended only for the use of the individual or entity named
above and may contain information that is confidential and privileged,
proprietary to the company and protected by law. If you are not the intended
recipient, you are hereby notified that any dissemination, distribution or
copying of this e-mail is strictly prohibited. Opinions, conclusions and
other information in this message that do not relate to the official
business of our company shall be understood as neither given nor endorsed by
it.

[Luigi Ballabio-2]

At 04:29 PM 4/30/03 +0200, Andre Louw wrote:
>One more thing, in the inheritance tree, IndexedCoupon has both InArrear,
>and UpFront Coupons inheriting from it. ParCoupon has nothing, is this
>portion still missing or am I missing something? Is it not possible to have
>a "par" coupon fixing at the end?

Right, it's not possible. A par coupon has too much constraints.

Bye,
         Luigi

[Nicolas Di Césaré]

Le mer 30/04/2003 à 15:48, Luigi Ballabio a écrit :

> At 02:58 PM 4/30/03 +0200, Andre Louw wrote:
> >Can you explain to me the difference between a Par Coupon and an Indexed
> >Coupon?
>
> Andre,
>          due to holidays and rolling conventions, the end date of a coupon
> starting at a given date might not match the end date of the corresponding
> Euribor deposit starting at the same date. Example: take a 5-year sequence
> of semi-annual coupons starting May 5, 2003 on the TARGET calendar. Their
> start/end dates are:
>
> May 5th, 2003
> November 5th, 2003
> May 5th, 2004
> November 5th, 2004
> May 5th, 2005
> November 7th, 2005
> May 5th, 2006
> November 6th, 2006
> May 7th, 2007
> November 5th, 2007
> May 5th, 2008
>
> so that, for instance, the penultimate coupon starts May 7, 2007 and ends
> November 5th, 2007. But the 6-months Euribor fixing of May 7, 2007 is based
> on a deposit with end date November 7th, 2007!
> ParCoupon and IndexedCoupon are two different approaches to this date
> mismatch, namely:
>
> let's call "start" the start date, "end_1" the end date of the coupon, and
> "end_2" the end date of the deposit underlying the Euribor fixing.
>
> 1) ParCoupon calculates the coupon rate as
>          rate = (discount(end_1)/discount(start) - 1)/T
>     where T is the period between start and end_1. This has the advantage
>     that the NPV of a bond nicely adds up to 100 when the redemption is
>     included, and that each rate is paid for the exact period over which
>     it is calculated---i.e., no convexity. However, when May 7th, 2007 comes,
>     the coupon will fix based on the underlying deposit dates!
>
> 2) IndexedCoupon forecasts the coupon rate based on the deposit, i.e. as:
>          rate = (discount(end_2)/discount(start) - 1)/T
>     where T is the period between start and end_2. This is the rate as will
>     be fixed when May 7th, 2007 comes. However, it will be accrued over a
>     different period, namely, between start and end_1, which introduces a
>     small convexity error.
>
> Therefore, IndexedCoupon accrues wrongly the right fixing, while ParCoupon
> accrues rightly the wrong fixing. As I never sat down to try and estimate
> which error is smaller, I'm not suggesting that either is best...
>

Hi all,

the accrual period T is also different because different daycounters are
used. ParCoupon uses termStructure daycounter and IndexedCoupon uses
index daycounter.


--
Nicolas Di Césaré <[hidden email]>