FRA and cap pay off differences

Hi all,

I just wonder what is the explanation of the difference in payoff of FRA and Cap option. Both in FRA and Cap actual payment is made x days after expiration date (i.e. 90 days when contract is based on 90-day LIBOR)

My question is about discount.

In FRA we do have to discount the payoff amount at date of expiration for above mentioned 90-days using 90-days LIBOR rate at the expiration.

On the contrary, while calculating Cap payoff we don’t. We just calculate payoff as (strike rate - LIBOR) * principal *90/360 in our example.

I am confused why shouldn’t we discount the cap value as well as payoff is actually paid 90 days after expiration date (the same as in FRA) ?

Correct me if I am wrong, and forgive me any mistakes I just did.

Thank you in advance for any help.

Regards,

Mateusz

I believe that caps (and floors) are paid in arrears; e.g., a cap based on 90-day LIBOR would be paid 90 days after the expiration of the cap, and the payment would not be discounted.

FRAs, contrariwise, are paid in advance; e.g., an FRA based on 90-day LIBOR would be paid upon expiration of the FRA; the payment would be calculated as if it were paid after 90 days, then discounted back 90 days to the expiration of the FRA.

So in the FRA you get the payoff 90 days sooner than in the cap/floor, but it’s discounted.

Thank you for this explanation. Seems I understood it incorrectly as I thought FRA was paid in arrears as well.

Glad to be of help. You’re quite welcome.

S200magician,

Could you please give an example to understand the following statement: " With a swap, the next payment, is always known one period ahead, when the floating rate for the next period becomes known".

I really dont get it…

I think Im getting the main difference between FRA and SWAP, which is that the exchange of payments for a FRA occurs at expiration and for swap occurs at the maturity of the X-day LIBOR?

Why do you discount me by 90%?

Suppose that you have a semiannual pay swap, based on 6-month LIBOR. The payment 6 months after inception will be based on the 6-month LIBOR rate in effect at inception, so you know both the fixed rate and the floating rate immediately. The month 12 payment will be based on the 6-month LIBOR rate in effect at the end of month 6 (when you make the first payment), so, again, you know both the fixed rate and the floating rate at the start of the period. And so on. The (floating) rate is known in advance (at the beginning of each 6-month period) but paid in arrears (at the end of each 6-month period).

Thank you again S200magician.

What about a FRA, can you please put an example as clear as the one you put for a Swap?

Thank you!!