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eqderiv
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Posts: 3
Joined: July 14th, 2002, 3:00 am

IR Option Vol Interpolation

January 10th, 2003, 2:30 pm

If I have a strip of CAP vols (quoted out of spot) then what is the mathematics to calculate the volatility for any CAP starting at any time. For example, if I have the following vols from ICAP's page for a 3.0% and 3.5% CAP on 6m EURBIOR:1y 25.2% 25.9%2y 26.5% 25.4%3y 25.6% 23.6%4y 24.9% 22.4%5y 24.2% 21.6%6y 23.5% 20.9%I now want to work out the correct CAP vol to price a 5y 3.25% CAP which starts in 2mths time.If I want to use the correct CAP vol then how would I calculate this, without calculating all of the CAPLET vols? Is there a simple solution? and if so what are the mathematics?Thanks in advanceEqDeriv
 
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Val
Posts: 23
Joined: June 5th, 2002, 12:51 pm

IR Option Vol Interpolation

January 10th, 2003, 4:18 pm

if I understand you correctly, you want to price a forward start cap .In that case you will need a foward foward volatility structure of 6M EURIBOR.In Black approach, the only way to price it, is, first of all, to boostrap the spot volatility term structure and after using the relation between spot and forward vols to calculate your 2 mths forward vol term structure.One solution to your issue would be to a short rate model, which can directly be calibrated to cap prices.Hope it will help.
 
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mj
Posts: 12
Joined: December 20th, 2001, 12:32 pm

IR Option Vol Interpolation

January 11th, 2003, 2:34 pm

Quote[Is there a simple solution?noMJ