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# Interest rate cap and floor

### Interest rate cap and floor Definition

An interest rate cap is a series of European call options or caplets on a specified interest rate, usually the LIBOR interest rate. The underlying rate is known as the reference rate. The buyer of the cap receives money if on the maturity of any of the caplets, the reference rate exceeds the agreed strike price of the cap.

In formulas a caplet payoff on a rate L struck at K is

Nαmax(LK,0)

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 2005 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.

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 below the agreed strike price of the floor.

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