Is selling a payer swaption = buying a receiver swaption?

I know the answer is No - because a receiver option is a call on bond prices (i.e. that interest rates will drop), and a payer option is a put on bond prices. Call and negative Put payoffs are not quite symmetric.

However, I know that selling a payer swaption means giving the couterparty the right to pay-fixed and recieve floating. Since I sold the payer swaption I am paying floating.

A receiver swaption is the right to receive fixed and pay floating.

Is the only difference the ownership of the exercise right? They seem like they’d offer similar hedging benefits.

They offer similar but opposite benefits. Buying a payer swaption will cost you premium, selling it will earn you premium.

No it is completely difference…the first is a right and the second is an obligation…

Now, if rate go up, the buyer of receiver swaption get nothing, the option is out of money…

the seller of payer swaption has to receive low fixed rate and pay higher floating rate, he lose money…

^ You are right, they are no way similar. By buying an option you shed the risk and by selling it you take on the risk. Thanks for clarifying. Makes me think, how easily we could arrive at a wrong conclusion.