Interest rate swap and interest rate option

A payer interest swap = Long an interest rate cap and short AND short an interest rate floor.

I think it should be OR not AND. both long interest cap and short interest floor is good when interest increase but why need both long cap and short floor to be equal to a swap.

Please add comments

Hey think of it like this…

Lets say, swap fixed rate is 5%

profit and loss on the fixed rate swap is linearly related to the level of interest rates at expiration. For example, if rates move to 6%, then the payoff is 1%. If rates move down to 4%, then the loss is -1%.

We want to exactly replicate this payoff profile with options in order to claim equivalency.

position we take is:

Long interest rate cap with a strike of 5% and short interest rate floor with a strike of 5%

If rates go to 6%, exercise cap (caplet) for profit of 1%, short floor expires worthless

If rates go to 4%, get exercised on floor (floorlet) for loss of 1%, long cap expires worthless

If we have long cap and short floor, both with strikes at 5%, then this is equivalent to pay fixed swap at 5%.