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Total Posts: 6
Joined: Apr 2017
Posted: 2017-06-10 20:30
I believe that this topic has been posted on a decent amount before but I'm looing for some help with the formula and notations. I'm just looking for the simple black model to price a cms curve cap option. I have derived the curve cap vol from swaption vols for each forward tenor and correlations between the forward tenors. I have also calculated the convexity adjustment on the two rates. I'm pricing a 6month forward 10yr/30yr atm curve cap. For the inputs i have:
(these numbers are approximate)
6m10yr 2.05 and vol of 60 annualnormvol
6m30yr 2.30 and vol of 55 annualnormvol
spread of 25bps with a convexity adjustment of 1.5bps so atm strike of 26.5. I used about 96% correlation and got a vol of 18bps. In addition, let's say the 6month discount rate is 1.40%.

So can someone help me to calculate the curve cap price using these inputs? The actual calculation and not just the formula is what im looking for since that's part of my issue. Of course i'll be doing this in excel and the inputs given here may not tie out to what i say i've calculated since I was just trying to remember them but they can be taken as correct. Thank you!
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