Posted by
Nicolas Di Césaré on
Apr 30, 2003; 11:21am
URL: http://quantlib.414.s1.nabble.com/ParCoupon-class-tp2503p2505.html
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]>