Premium of Receiver Swaption

The higher the excercise rate of a receiver swaption, the higher the premium of the receiver swaption?

correct, without the need to go into valuation

if you hold the right to at a point in time enter to pay the market rate and get 6%

vs teh right to pay the market rate and get 10% clearly all else equal the one that gives you the right to get more is worth more

receiver swaption is a right to enter on receive fixed-pay floating swap

when would you like to receive fixed & pay floating => when int rate goes down

So higher the execercise rate, more its become valuable => higher premium

It’s always the fixed side. Receive = fixed. Payer = fixed.

Now get to learn how to add/remove options from callable/non-callable bonds using swaptions. Fun stuff, but important.