# short question on collars

Which of the following is equivalent to a pay-fixed interest rate swap? A) Buying a cap and selling an interest rate collar. B) Selling a cap and buying a floor. C) Buying a cap and selling a floor. Your answer: A was incorrect. The correct answer was C) Buying a cap and selling a floor. A pay-fixed interest rate swap has the same payoffs as a long position in the corresponding interest rate collar (with the strike rate equal to the swap fixed rate). here is my question…if cap and floor rates are the same, i see how you replicate the fixed payments…but in a pay fixed swap, you are also receiving floating rate payments…how is that replicated by buying a cap and selling a floor? for example, say cap and floor rates are 5%. if rates go above 5%, you will always pay 5% due to the cap. if rates go below 5%, you will still pay 5% do to the floor. waht about the floating rate receipts? seems like buying a cap and selling a floor of the same strike rate only replicates a fixed rate bond.

Let’s see: The swap settles a floating rate against a fixed rate, and the net interest generates a cash flow 1 period later. If floating rate rises beyond the swap fixed rate , the pay-fixed receives a payment The cap buyer receives a payment whenever the floating rate exceeds the strike ( which is same as swap fixed rate ). That is the meaning of cap , after all , the buyer is paid when floating exceeds collar strike .So swap is same as cap for rates above the strike . Next when rates drop below strike , the swap fixed pays the swap floating the difference. On the floor side , the seller of the floor who is nothing but same collar holder pays the counterparty the difference between the strike and the floating . That is after all the meaning of a floor ( seller pays buyer when rates fall below strike). So the floor cash flow is same as the swap cash flow. Therefore with one instrument i.e. a swap , we are replicating a buy-cap/sell-floor deal, i.e. we are replicating a collar

1. The pay-fixed leg of an interest rate swap is long on rate; 2) cap is call on rate; floor is put on rate. (caplets/floorlets) So the answer is C). This is similar: long stock == buy call + sell put.

A pay fixed rec floating swap has negative duration, so it benefits when rates increase. Among the choices given, only buy a cap and sell a floor will benefit from rates increase.

ok got it. this is essentially what we learned in level 2 swaps material…that a pay fixed swap is equal to a long call and short put. thank you guys.