Let an implied volatility curve/surface is made up by optionlets or swaptions Black's implied volatility.
If you wanted to price, say, a FRN with cap and/or floor, a CMS et cetera you would input the array/matrix filled by that IV curve/surface in you pricing model: regardless of the model, it's very likely it takes as input that curve/surface.
- is it actually possible to find a constant volatility value which returns a fair value close enough to the one obtained via curve/surface? (*)
- If said value existed, how would it be? Could it be a weighted average of all the curve/surface implied volatilities? Or just the ATM ones?
- If said value existed and it could be expressed by a weighted average, how the weights should be? Maybe something related to swaptions options & swap tenors? Something else?
(*) When I say «close enough» I mean that I would be okay with a rough and/or heuristic proxy, too. I do not actually need any accurate value.