For valuation of Swaptions before expiration, CFA text book has provided the below formula:
Payer swaption = (AP)PVA[RFIXN(d1) - RxN(d2)] Receiver swaption = (AP)PVA[RxN (-d 2) - R p^N f-dj)] where: PVA = PV of annuity matching the forward swap payment based on a notional amount of 1 AP = Accrual period RFiX = Market swap fixed rate (annualized) at the time of swaption expiration (t = T) R x = The swaption exercise rate starting at Time T, again quoted on an annual basis. As before, we will assume a notional amount of 1. G = Volatility of the forward swap rate. Specifically, it represents the annualized standard deviation of continuously compounded percentage changes in the forward swap rate.
I am really confused with the above formula because it values swaption before expiration. Since the present value of annuity factor(PVA) covers the period after expiration. So why don’t we need to discount it back to today’s date/Valuation date?
I have come across the below formula & it makes sense as against the formula provided by CFA Institute.
http://janroman.dhis.org/finance/Interest%20Rates/swaptions.pdf