I have a very "simple" question but I think the answer is not completely straightforward:
"What historical volatility would you compare to the implied volatility of a standard Swaption (priced with Black-76 formula)?"
That is, totally disregarding how to estimate the volatility (in the sense of GARCH, bayesian, time periods and so on ...) what data would you use, for example, for a 3m10y Swaption? would you use the historical series of the corresponding spot interest rate swap, the 10y swap rate? Or the historical volatility of the corresponding forward swap, the 10y swap 3m forward? Or something else?
The natural extension is (and the original question was) :
"What historical volatility would you use to price a Midcurve Swaption (that is an option to enter into a forward starting swap)?"
Same as before, what data series would you use (or construct) to estimate this volatility?
Thanks in advance =)