Is selling a payer swaption = buying a receiver swaption?

CFA Level III Derivatives
#1

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.

#2

Think of selling payer swaption vs selling receiver swaption + receiver swap?

#3

The hedging beneits between selling a payer vs buying a reciever differ greatly. The first has negative convexity and the latter has positive convexity. Selling a payer option has unliminted loss if rates increase vs buying a receiver has limited loss of the premium if rates increase and unlimited gain(constrained by the level of rates) if rates decrease. As a result they will have differing deltas, differing durations and opposite convexity exposures.