QuantLib › quantlib-users

Re:Question on Caps/Floors pricing on InArrear cashflows.

Classic

List

Threaded

3 messages Options

enrico.michelotti

Re:Question on Caps/Floors pricing on InArrear cashflows.

The CashFlow vector created with InArrearCoupon is corrected,
since the InArrear cap/floor resets at the end of each accrual period when the payment is done (apart for the adjustment of a rolling date).
The only problem is that you cannot anymore use the simple Black pricing, but you need an adjustmnet for the convexity effect.
If I do remember well in Brigo-Mercurio you can find such adjustment.

Enrico
---------- Initial Header -----------

Toyin Akin

Re:Question on Caps/Floors pricing on InArrear cashflows.

Hi,

Thanks for the quick reply.

A few more further questions for you if I may...

Are you saying that for the In-Advance Cap (Brigo-Mercurio pg 379) the
exercise date of each caplet
is equal to the reset and payment dates?

Also, there is already a convexity adjustment applied to the rate due to the
fixing effect
within the Inarrearindexedcoupon class, From my first initial pass from
Brigo-Mercurio there is indeed a correction term added to the original
black-scholes formula ( BS() ).

However there doesn't seem to be the correction term that the
Inarrearindexedcoupon class has applied to the rate ( within Brigo-Mercurio,
BS() is applied to an unadjusted rate and then a correction term added to
the premium ).

If the fixing date is at the beginning of the period and one has already
applied an adjustment to the rate, does one need to apply an adjustment to
the BS() formula.

Best Regards,
Toyin Akin.

>From: "enrico.michelotti" <[hidden email]>
>To: "quantlib-users" <[hidden email]>
>Subject: Re:[Quantlib-users] Question on Caps/Floors pricing on InArrear
>cashflows.
>Date: Tue, 4 Oct 2005 08:22:58 +0200
>
>The CashFlow vector created with InArrearCoupon is corrected,
>since the InArrear cap/floor resets at the end of each accrual period when
>the payment is done (apart for the adjustment of a rolling date).
>The only problem is that you cannot anymore use the simple Black pricing,
>but you need an adjustmnet for the convexity effect.
>If I do remember well in Brigo-Mercurio you can find such adjustment.
>
>Enrico
>---------- Initial Header -----------
>
>From : [hidden email]
>To :
>[hidden email],[hidden email]
>Cc :
>Date : Tue, 04 Oct 2005 07:03:09 +0100
>Subject : [Quantlib-users] Question on Caps/Floors pricing on InArrear
>cashflows.
>
>
>
>
>
>
>
> >
> > Hi all,
> >
> > Within Quantlib you can create an array of cashflows which can then be
> > passed into the CapFloor constructor.
> >
> > My question is whether the pricing logic within the CapFloor class is
> > correct for InArrear cashflows?
> >
> > The CapFloor class takes as it's exercise date for all the
> > caplet's/floorlet's the fixing date of the coupon.
> >
> > Under a UpFrontIndexedCoupon this would be settleDays before the start
>date
> > of the period.
> > Under an Inarrearindexedcoupon this would be settleDays before the end
>date
> > of the period.
> >
> > Thus when pricing a caplet/floorlet which is based on an
> > Inarrearindexedcoupon, should the
> > exercise date still be settleDays before the start date of the period?
> >
> > My guess is that the exercise date should be settleDays before the start
> > date of the period.
> >
> > Best Regards,
> > Toyin Akin.
> >
> >
> >
> >
> > -------------------------------------------------------
> > This SF.Net email is sponsored by:
> > Power Architecture Resource Center: Free content, downloads,
>discussions,
> > and more. http://solutions.newsforge.com/ibmarch.tmpl
> > _______________________________________________
> > Quantlib-users mailing list
> > [hidden email]
> > https://lists.sourceforge.net/lists/listinfo/quantlib-users
> >
>
>
>
>-------------------------------------------------------
>This SF.Net email is sponsored by:
>Power Architecture Resource Center: Free content, downloads, discussions,
>and more. http://solutions.newsforge.com/ibmarch.tmpl
>_______________________________________________
>Quantlib-users mailing list
>[hidden email]
>https://lists.sourceforge.net/lists/listinfo/quantlib-users

Toyin Akin

Re:Question on Caps/Floors pricing on InArrear cashflows.

In reply to this post by enrico.michelotti

Enrico,

Thanks for the info.
I have a better understanding of this now.

However it should be noted that anyone passing an in-arrears leg into the
CapFloor class will
generate unadjusted premium values.

Best Regards,
Toyin Akin.