Posted by
Toyin Akin-4 on
Oct 21, 2002; 8:11am
URL: http://quantlib.414.s1.nabble.com/RE-Delta-on-Capfloor-tp2259p2263.html
Whoops
regarding this paragraph
> I don't really have all the calculations for the above and not really sure
> how the swap bpv is calculated, but lets say we have a very in the money
> option (strikes at 0.5, not assuming JPY), assuming that the swap bpv
> remains the same above, and the deltas are all 1.0 we'll now have
3*notional
> / 1BP as the final value. Again (protecting myself here!!) I'm not sure
how
> you have computed the 0.45 in the 6M swaps's bpv calc above, but I assume
> it's independant of the option's strike.
It's not 3*notional / 1BP, but 2.02*notional / 1BP.
Basically greater than 1.
Regards,
Toy.
----- Original Message -----
From: "Toyin Akin" <
[hidden email]>
To: <
[hidden email]>
Cc: "'Andre Louw'" <
[hidden email]>; "Perissin Francesco"
<
[hidden email]>; "QuantlibUsers (E-mail)"
<
[hidden email]>;
<
[hidden email]>
Sent: Monday, October 21, 2002 3:01 PM
Subject: Re: [Quantlib-users] RE:Delta on Capfloor
> Hi all,
>
> > Andre, you're right to compare the swap sensitivity to the cap's one.
> > This is the same structure: a Swap is serie of FRA and a caplet is an
> > option on FRA. Exactly like comparing the option on Equity and the
Equity.
> > this is what traders are doing: hedging CAP/FLOOR with Futures and Swap
or
> > the opposite.
>
> I agree that in the equity case comparing the option on Equity and the
> Equity makes sense, the underlying of the
> equity option *IS* the equity.
>
> Maybe I'm missing the point somewhere but...
>
> The underlying for a caplet is a single FRA, not a series of FRAs.
> An option on a series of FRA's is a swaption.
> Several options where the underlyings are FRA's is a cap.
>
> The underlying of a cap is not a swap.
>
> Now I haven't looked at the history of this exchange, but... if the
question
> you are all asking is that you want to hedge the cap's delta with a swap
and
> not why does the cap's delta's sum, sum to more than 1, then yes, you
could
> hedge with any instrument, the most liquid being FRA's, futures, swaps or,
> if one really wanted to, any option where you want to introduce
gamma/vega.
> You just need to take into account the hedge instruments sensitivity.
>
> The reason why we pick Deposit,s FRA's, futures, swaps to hedge is because
> these are the most liquid instruments and
> our yield curve is composed of these instruments. Thus all we need to do
is
> to find the right ratio to hedge.
>
> But in answer to the original question... as to why the total delta of a
cap
> sum could be more than 1... you really have a portfolio of options.
>
> > Taking your example:
> > Caplet 1 (6 months) has delta of 0.6 => delta* swap 6M bpv = 0.6* 0.45
*
> > notional/1 BP (around that)
> > Caplet 2 (9 month) has a delta of 0.5 => delta* swap 9M bpv = 0.5* 0.67
*
> > notional/1BP
>
> > Caplet 3 has a delta of 0.4 => delta* swap 1Y bpv = 0.4*0.9 * notional/
> 1BP
> > Summing these gives 0.965*notional / 1BP that is to say almost 100% of
the
> > 1Y swap sensitivity isn't it?
>
> I don't really have all the calculations for the above and not really sure
> how the swap bpv is calculated, but lets say we have a very in the money
> option (strikes at 0.5, not assuming JPY), assuming that the swap bpv
> remains the same above, and the deltas are all 1.0 we'll now have
3*notional
> / 1BP as the final value. Again (protecting myself here!!) I'm not sure
how
> you have computed the 0.45 in the 6M swaps's bpv calc above, but I assume
> it's independant of the option's strike.
>
> Also is the swap 1Y bpv an ATM swap from spot up to one year? If so you
can
> see immediatly that we are dealing
> with different structures. Caplet 3 is an option on a 3M FRA... one
fixing.
> The swap 1Y is a swap with 4 FRA's.
>
> Regards,
> Toyin Akin.
>
> ----- Original Message -----
> From: <
[hidden email]>
> To: "Toyin Akin" <
[hidden email]>
> Cc: "'Andre Louw'" <
[hidden email]>; "Perissin Francesco"
> <
[hidden email]>; "QuantlibUsers (E-mail)"
> <
[hidden email]>;
> <
[hidden email]>
> Sent: Monday, October 21, 2002 1:26 PM
> Subject: Re: [Quantlib-users] RE:Delta on Capfloor
>
>
> >
> > Hi All,
> > Andre, you're right to compare the swap sensitivity to the cap's one.
> > This is the same structure: a Swap is serie of FRA and a caplet is an
> > option on FRA. Exactly like comparing the option on Equity and the
Equity.
> > this is what traders are doing: hedging CAP/FLOOR with Futures and Swap
or
> > the opposite.
> >
> > Now what you forgot is to multiply each caplet sensitivity by the swap
BPV
> > (the sensi for 1BP change in the IR curve) because the delta of a caplet
> is
> > not in % but calculated for a move of the underlying.
> >
> > Taking your example:
> > Caplet 1 (6 months) has delta of 0.6 => delta* swap 6M bpv = 0.6* 0.45
*
> > notional/1 BP (around that)
> > Caplet 2 (9 month) has a delta of 0.5 => delta* swap 9M bpv = 0.5* 0.67
*
> > notional/1BP
>
> > Caplet 3 has a delta of 0.4 => delta* swap 1Y bpv = 0.4*0.9 * notional/
> 1BP
> > Summing these gives 0.965*notional / 1BP that is to say almost 100% of
the
> > 1Y swap sensitivity isn't it?
> >
> > Bye
> > Xavier
> >
> >
> >
> >
> > "Toyin Akin"
> > <
[hidden email]> To:
> "Perissin Francesco" <
[hidden email]>, "'Andre
> > Sent by: Louw'"
> <
[hidden email]>, "QuantlibUsers \(E-mail\)"
> >
[hidden email]
> <
[hidden email]>
> > eforge.net cc:
> > Subject:
> Re: [Quantlib-users] RE:Delta on Capfloor
> >
> > 21/10/2002 13:13
> >
> >
> >
> >
> >
> >
> > Hi again,
> >
> > In addition, a cap structure being a portfolio of caplets does not
include
> > information regarding the correlation being
> > the individual FRA's. You'll need to look at swaptions for this.
> >
> > I may be wrong here but I wouldn't try to compare a swap's sensitivity
to
> > that of the cap's.
> > The 2 numbers really account for different measures of risk.
> >
> > compare swap sensitivity with that of swaptions
> > compare a FRA's sensitivity to that of caplet's
> > a series of FRA's sensitivity (which really is a swap) should thus be
> > compared to swaptions.
> >
> > Regards,
> > Toy.
> >
> > ----- Original Message -----
> > From: "Toyin Akin" <
[hidden email]>
> > To: "Perissin Francesco" <
[hidden email]>; "'Andre
Louw'"
> > <
[hidden email]>; "QuantlibUsers (E-mail)"
> > <
[hidden email]>
> > Sent: Monday, October 21, 2002 11:54 AM
> > Subject: Re: [Quantlib-users] RE:Delta on Capfloor
> >
> >
> > > Hi all,
> > >
> > > Remember, a cap is a series of caplets. thus you are buying a
portfolio
> > of
> > > options.
> > > Like any portfolio of options, the sum of the deltas, which will be
your
> > > total sensitivity if rates move can
> > > be well over 1.0. However the delta of any *ONE* caplet will be <= +-
> > 1.0.
> > >
> > > If each caplet is well in the money, then each caplet will have a
delta
> > of
> > > 1. Thus the sum will be above one.
> > >
> > > Also, a caplet is an option on an individual FRA. Thus you cannot
really
> > > bring swaps into this.
> > > You may be confusing swaptions with caps here.
> > >
> > > A swaption is an option on a swap.
> > >
> > > Regards,
> > > Toyin Akin.
> > >
> > >
> > > ----- Original Message -----
> > > From: "Perissin Francesco" <
[hidden email]>
> > > To: "'Andre Louw'" <
[hidden email]>; "QuantlibUsers (E-mail)"
> > > <
[hidden email]>
> > > Sent: Monday, October 21, 2002 11:13 AM
> > > Subject: RE: [Quantlib-users] RE:Delta on Capfloor
> > >
> > >
> > > >
> > > > Hi,
> > > >
> > > > >The answer given originally to my question on calculating the delta
> on
> > a
> > > > >capfloor structure was that it is simply the sum of the delta's on
> all
> > > the
> > > > >caplets (assuming flat nominals, there is no weighting needed).
> > > >
> > > >
> > > > I gave you this answer assuming another definition of delta for an
> > > interest
> > > > rate instrument, i.e. the change in present value given a parallel
> > shift
> > > of
> > > > 1bp in the used curve. Also, this is quite close to the change
obtaine
> d
> > by
> > > > shifting of 1bp the prices of the benchmarks used to bootstrap the
> > yield
> > > > curve.
> > > > This seems to be equal to what you name "sensititvity", is it right?
> > > >
> > > > Regarding the definition that you are referring to, (i.e. the cap
> > > > sensitivity divided by the IRS sensitivity) I have to think a while
> > about
> > > > it. The example could help.
> > > >
> > > >
> > > >
> > > > >e.g I have a 3Mx12M, 3 monthly cap, which results in 3 caplets,
> > results
> > > as
> > > > >follows:
> > > > >the 1st strikes at a delta of 0.6, the 2nd strikes at a delta of
0.5,
> > the
> > > > >3rd at a delta of 0.4. Summing these gives 1.5E
> > > >
> > > >
> > > > Just for understanding, do you mean that the first fixing is in 3
> > months
> > > ans
> > > > last fixing in 9 months? Which curr? Which strike?
> > > > In any case, it's not correct to sum the deltas (according to your
> > > > definition). I would be tempted to say that you should sum the
caplet
> > > > sensitivities in order to get the cap sensitivity. Now you could
> divide
> > > the
> > > > result by the IRS sensitivity, isn't it?
> > > > Let me know it this can help...
> > > >
> > > >
> > > > >Ok, maybe it's on the Delta with respect to spot: the above caplets
> > gives
> > > > >0.13, 0.11, 0.08, giving a total of 0.32, (doesn't 'feel' right!),
> > > > depending
> > > > >on the termstructure and the length of the cap, the sum of the
> > > spot-delta's
> > > > >quite often goes over 1.0!
> > > >
> > > >
> > > > Andre, I could not understand this... could you try to explain again
> > the
> > > > above numbers?
> > > >
> > > >
> > > > Ciao
> > > > Francesco
> > > > --
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