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Receiver Swaption equivalent to call option

I know I could just memorize that a receiver swaption is equivalent to call option, but I can't rationalize it...

Isn't it true that in a receiver swaption the person receives fixed and pays float, so gain is to be made when interest rate drops. Doesn't this seem more like a put option?

Are you sure you don't mean a call option on the fixed income bond? (i.e. Not interest rate option, but on the price of the bond itself.)

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