I am trying to estimate the (annualized) volatility that should go into an European Swaption (such as 2y5y). Given we take the black76-formula, where the discounting is the term outside the expectation, and the pricing formula has the (a) the drift term i.e. the Forward, and (b) the distribution with the volatility term.
If I extract a time-series of the 2y5y forward rates, I would like to ask what should I use to estimate the volatility. Would it be
- he (excel) stdev function which is taking (Summation(Xi - Xmean)^2) / n; or
- the summation of the square of the realized daily moves... Summation(Xi^2)
Kind regards Kian