Re: RE:Delta on Capfloor

Posted by Xavier.Abulker on Oct 22, 2002; 2:22am
URL: http://quantlib.414.s1.nabble.com/RE-Delta-on-Capfloor-tp2259p2260.html

Hi Toyin,
A swaption is an option to enter into a swap at a given date.
for example if you have the option to enter in a 5Y swap in 1Y then if you
exercice this option once you enter in the swap there is no option anymore.
In 1Y you enter in a 5Y swap and whatever are the futures rates there is no
option anymore.
This is not exaclty the payoff of a cap: the cap is sum( max(forward -
strike,0)) but the payoff of a swaption is max(Swap NPV,0).

Now you already know that the put-call parity between cap and floor is Cap
= Floor + Swap, this is why the Cap delta is expressed in term of Swap BPV.

I absolutely agree that the cap is the sum of caplet and each caplet has to
be valued separately but if you take the B&S valuation for each caplet, the
B&S RAW delta is between 0 and 1 but is expressed in term of Swap BPV. (at
least this is what banks are doing in France and Germany!)

For example a delta of 0.5 for one caplet is not 0.5 EUR but 0.5 EUR per
Swap BPV. It means that from a delta of 0.5 you find the delta in currency
multiplying the B&S delta by the swap BVP then you can sum the delta of
each caplet and compare this value to the delta of a swap or a future or
even a swaption if you wish. I think this is what Andre was trying to do.

How I found the swap BPV: simple.

As you said the swap 1Y is a swap with 4 FRA's but taking a swap at the
break even (NPV=0) the swap is also:
A Notional exchange + fix flows.