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
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?