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that's it right there. I just packed that freakin' statement and locked it on the right side of my brain until Saturday at 4:05PM.

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it is equivalent to a call option on a bond because they both benefit when interest rates fall. in a receiver swaption, you pay floating and receive fixed, therefore your betting on rates to fall.

similarly in a call option in a bond , you are betting that interest rates will fall, hence you get to buy the bond at cheaper price. remember that the price of bonds and interest rates are inversely related.

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receiver swaption = right to receive fixed-rate = valuable if interest rate falls = call option on bond

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