Posted by
Luigi Ballabio on
URL: http://quantlib.414.s1.nabble.com/Possible-problem-on-bermuda-swaptions-2-tp3621p3634.html
On 02/24/05 15:05:24, Luca Berardi wrote:
>
> Luigi, thanks for the mail. I had quick look at the patch and have
> some comments:
>
> 1) you are silently assuming that exercise dates coincide with payment
> dates of the underlying swap. Of course there might be some
> de-synchronization due to dates adjustment as you pointed out, but
> still it's not possible to deal with cases where the exercise dates
> are quite different from the swap's payment dates. The trader I
> talked to, told me that usually exercise dates are ten (business)
> days before the payment dates of the underlying swap, and with the
> adjustment carried out through the new adjust() method you cannot
> take into account such a long temporal shift. Of course it could be
> possible to extend the adjustment for a period longer than a week,
> but then you get a mispricing due to moving payment dates to
> exercise dates. In general it would be nice not to require that
> exercise dates must "roughly" coincide with the dates in the
> underlying swap's schedule.
Yes. The point of the patch was more to avoid mispricing in the current
state of affairs---exercise dates some days in the past should be treated
differently.
> 2) It's ok to shift backwards the payment dates of the fixed leg to
> match the exercise dates, but why do you need to shift the fixing
> dates of the floating leg forward (again to match the nearest
> exercise date)?
Because due to the way the floating-leg coupons are priced on the tree,
during rollback they are added to the swap at their fixing date rather than
at their payment date. A fixing date two days before an exercise date
refers to a payment happening six months or one year later, which is
included in the swap the option holder is possibly entering into. If the
date is not corrected, the exercise condition is applied before adding such
payment.
> Still on the exercise dates issue:
>
> Assume for simplicity that the floating and fixed leg of the
> underlying swap have the same schedule. In pricing the bermuda
> swaption one should discard the very successive payment after the
> current exercise date.
> If the floating and fixed leg have different schedules (e.g. funding
> leg pays quarterly and fixed annually) things get more complicated
> because all the swap cashflows following the current exercise dates
> must be discarded until we reach the second cashflow of the lower
> frequency leg.
Why the second cashflow? Let's say you have a swaption with exercise today
(Feb. 24, 2005) and the underlying swap paying annual fixed coupons and
receiving quarterly floating coupons. It is my understanding that if the
swaption were exercised, the holder would enter in a swap starting today;
i.e., he will not receive or pay coupons today (or the next few days) but
he will indeed receive floating payments in May 2005, August 2005, November
2005 and February 2006, and pay a fixed coupon in February 2006. Do you
think otherwise?
Later,
Luigi
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