# Swaption annuity factor

In H. Corb's book about interest rate swaps and oder derivatives, the present value of an T into n payer swaption is given via

$$A\sigma\sqrt{T}\left[\frac{1}{\sqrt{2\pi}}e^{-\frac{d^2}{2}}+d\,\mathcal{N}(d)\right]$$

where

$$A=\sum\limits_{t=T+1}^{T+n}\mathrm{DF}(0,t)$$

is the annuity factor.

I understand the sum in such a way, that it reflects the discounting of all cash flows following the first year after option expiration ($$T+1$$) up to the ending of the swap ($$T+n$$).

However, it strikes me that this might assume an interest rate swap with only annual cash flows. What about IR swaps with distinct and different leg frequencies, like semi-annual for the fixed leg and quartlerly for the floating leg.

Summarized, is the annuity factor the sum of all discounted cash flows?