ningning1984

I had this exact same problem. See if this helps.

1. Receiver swaption is a put option on interest rate. It is also a call option on Bond as you have mentioned. Why?

Suppose the fixed rate that you will receive if you exercise the option is 5%. Now market interest rates go down to 3%. You are a winner here. (also see that as interest rates go down bond prices increase). So,

Interest rates go down-->Receiver swaption valuable (Hence the put on interest rate)
Bond prices go up-->Receiver swaption valuable (Hence call option on bond prices)

*Receiver swaption also similar to floorlet since both benefit as interest rates go down.