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Suppose we know (from looking at an available volatility surface) the implied volatility (flat volatility) of a cap with a maturity of 10 years and strike of 1%. This would correspond to a cap that's spot starting, correct?

If we instead have a cap with a maturity of 10 years and strike of 1% that becomes active in 1 years time (so the cap runs from year 1-11), what is the correct implied volatility to use to value this? It feels to me that it must be different from the first situation, since we are finding the average volatility over a time period of an interest rate (as expected by the market) and we are now dealing with a separate time period. Would we have to strip the caplet volatilities from the surface and value each caplet contained in the second cap with these caplet volatilities? Or is there a shortcut?

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  • $\begingroup$ Given a CapFloor volatility surface, we can extract a Caplet/Floorlet volatility surface. This surface represents the Black (or Bachelier) volatility parameters to be entered into the Caplet/Floorlet pricing functions per expiry. Thus, given the CapFloor-Surface until 11Y expiry, you may back out the caplet/floorlet vols for the same range. HTH. $\endgroup$
    – Kermittfrog
    Oct 14, 2020 at 11:28
  • $\begingroup$ @Kermittfrog When you say back out the caplet vols, you mean caplet stripping, right? So if you wanted the flat vol for your forward starting cap, the process would be to: 1. Strip the cap surface to get the underlying caplet vols. 2. Value your forward starting cap with these caplet volatilities (so skipping the first 4 caplets for a 1 year starting one). 3. Use the price you have found (using the separate caplet volatilities) and calculate the corresponding flat volatility (one number) that when put into each underlying caplet retrieves the same price for the forward cap. Is that right? $\endgroup$
    – Oscar
    Oct 14, 2020 at 11:36
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    $\begingroup$ that would be my strong suggestion. I did not provide this as an answer because I have not yet seen how such a product is quoted in the market; that's why I only provided a comment (sorry). $\endgroup$
    – Kermittfrog
    Oct 14, 2020 at 15:34
  • $\begingroup$ Your strong suggestion is well appreciated nonetheless. $\endgroup$
    – Oscar
    Oct 15, 2020 at 8:09

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