# European Swaption Pricing Using Normal volatilities

On page 6 of this paper a forumla is given for payer swaptions, I am just wondering what is the formula for receiver?

My implementation of the formula for payer and receiver is here, but I am not very sure about it.

Also to get ATM swaption, does that mean the forward swap rate is equal to the strike price?

• for some reasons, the first link does not work – jherek Nov 20 '19 at 11:08
• The editor of the post made a mistake, I have corrected it now – hao Nov 20 '19 at 11:24

You can easily move from a payer ($$C$$) to a receiver ($$P$$) by using the put-call parity relationship: $$C(t) - P(t) = B(t,T) (F(t,T)-K)\,,$$
where $$B$$ is the discount factor to maturity, $$F$$ the forward rate, $$K$$ the strike.