I would like to know how the mid-curve swaption could inform us about forward volatility.
In my understanding it is a swaption on a forward starting swap.
Let us say the midcurve swaption expires in 1y. The underlying swap starts 1y after expiry and matures 10y latter. As the forward starting swap could be expressed as a bascket of a long 1y-11y forward swap and short 1y-1y forward swap.
In my opinion, all such a product expresses is the implied vols 1y-1y and 1y-11y swaptions and the correlation between thier underlyings.
So I don't get where the forward volatility comes from.