I am heading toward almost the end chapter of the Derivatives.

I have few questions that get me understood while trying to understand the topic.

So there is a concept called Equivalencies in Interest Rate Derivative contracts.

- Long interest rate call and short interest put is equivalent to Long FRA (receive floating, pay fixed)

My question is that I get that if you long interest rate cap, when the interest rate goes up, you get paid, when the interest goes down, you have to pay! so it is like receive floating. What I don’t get is “pay fixed”. you don’t really pay fixed amount when you long int. cap and short int. put. if the rate is the same, then you get noting and pay nothing. Isn’t it?

But why is it the same?

Similarly, if the exercise rate=current FRA rate, a short interest rate call and long interest rate put can be combined to form replicate a short FRA (pay-floating, receive fixed).

when the int.rate goes up, because I short interest cap, I have to pay for int. rate going up. when the interest rate goes down, because I long interest floor, I get paid!. so far so good. but i don’t receive fixed when I short int.cap and long int. floor. Isn’t it?

Thanks in advance, you are the Guru.