Interest rate cap
An interest rate cap is a derivative in which the buyer receives money at the end of each period in which an interest rate exceeds the agreed strike price. An example of a cap would be an agreement to receive money for each month the LIBOR rate exceeds 2.5%.
The interest rate cap can be analyzed as a series of European call options or caplets which exists for each period the cap agreement is in existence.
In formulas a caplet payoff on a rate L struck at K is
where N is the notional value exchanged and α is the day count fraction corresponding to the period to which L applies. For example suppose you own a caplet on the six month USD LIBOR rate with an expiry of 1st February 2007 struck at 2.5% with a notional of 1 million dollars. Then if the USD LIBOR rate sets at 3% on 1st February you receive 1m*0.5*max(0.03-0.025,0) = $2500. Customarily the payment is made at the end of the rate period, in this case on 1st August.
Interest rate Floor
An interest rate floor is a series of European put options or floorlets on a specified reference rate, usually LIBOR. The buyer of the floor receives money if on the maturity of any of the floorlets, the reference rate fixed is below the agreed strike price of the floor.