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anyone can provide solution or some idea to the following question? thanks

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Cap vols are normally quoted as a flat black or bachelier volatility that when used to price all the optionlets, will give the correct market price of the cap.

In your case, you will have to strip the caplet volatilities.

Example: you have the vol for the 1y cap and you have the vol for the 2y cap. Using the 1y vol for the caplets expiring the first year, find the vol for the caplets expiring in the second year that give you a market price equal to the 2y cap with a flat vol of the 2y vol.

Then use the same procedure for the 3y cap, with the 1y vol and the vol you found for the caplets expiring in the second year. Then same for 4th years and so forth...

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  • $\begingroup$ nice answer. What about the 0.25, 0.5 & 0.75 maturities though? Shall one assume flat vol for these maturities, equal to the 1Y vol? $\endgroup$
    – Jan Stuller
    Commented Jun 8, 2020 at 12:12
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    $\begingroup$ @Jan: Usually that's what I've seen so far, i.e. flat below the shortest cap maturity (1y mostly) and then between tenors it's flat with jumps at the 2y, 3y, etc. nodes... or linear interpolation in vol or var $\endgroup$
    – KevinT
    Commented Nov 23, 2023 at 11:17
  • $\begingroup$ @KevinT: thank you! $\endgroup$
    – Jan Stuller
    Commented Nov 23, 2023 at 12:51

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