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%.