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Napalm
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Joined: October 22nd, 2002, 9:42 am

At the money Cap

October 22nd, 2002, 9:49 am

Hi, SORRY for the dumb question, but i'm building up a simple excel pricer, chcking it against a pro system.I have a zero curve, and a swap one, a roll convention (6 months), a cap start date (spot) and a cap end date (5y)..How can I determine the ATM for that cap? That's not the forward rate, because the atm for a cap vs 6m is different from a cap vs 3m, it's not the swap rate for the same maturity (i have tried on my sytem..and it's not meaningful)...what else? How can i calculate the atm rate for a 5yrs cap??Regards,Napalm
 
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Pat
Posts: 28
Joined: September 30th, 2001, 2:08 am

At the money Cap

October 22nd, 2002, 12:15 pm

I believe that, by convention, ATM for caps is the swap rate corrected for frequency & dc basis.In the US, that means using the yield curve (discount factors!) to get the swap rate for a swap with quarterly Act360 fixed leg.You can rough out a conersion factor using (1 + 365rc/4)^4 = (1+rs/2)^2where rq is the quarterly cap rate and rs is the semiannual 30360 rateBy convention, a cap that's traded today does not include the first caplet ... since that caplet's payout has already been determined (or will be determined in a few hours). But I think this is not accounted in the ATM rate (ie, I think it is the spot 5y swap rate, not the 3m forward, 4.75y swap rate).Very (!) small discrepencies can be caused by not taking today's fixing into account in finding the swap rate (the swap's first floating leg payment is already set); not accounting for the basis spread (US 6m trades at spread of 0.625bps above the "true" rate, and other currencies have larger basis spreads; not having the correct holiday schedules or business day conventions
 
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Napalm
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Joined: October 22nd, 2002, 9:42 am

At the money Cap

October 22nd, 2002, 1:19 pm

Yep,Actually i found it myself with a little bit of thinking (and tweaking my spreadsheet): the correct ATM rate is actually the market rate for a swap with same dates as the cap (thus not spot, but frwd starting), with semiannual act/360 fixed leg (thinking about a 5yrs cap which is traded vs 6' )....that's not a plain vanilla swap...Thank you for your reply! (which went far beyond what i imagined...)Napalm
 
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Pat
Posts: 28
Joined: September 30th, 2001, 2:08 am

At the money Cap

October 22nd, 2002, 7:51 pm

I wouldn't mess with napalm