caps and floors

Can anyone explain this? Pg 328 in the derivatives section. “Buying a cap is equivalent to buying a package of puts on a fixed income security, and buying a floor is equivalent to buying a package of calls on a fixed income security.”

I’m confused because I thought a cap was = call and a floor = put.

There’s a difference between buying a call on an interest rate and buying a call on a bond: the former pays off when interest rates rise (and bond prices fall); the latter pays off when bond prices rise (and interest rates fall). Similarly for interest rate puts vs. bond puts.

Be careful!