Editing Interest rate cap and floor (section)

==Interest rate cap==
An '''interest rate cap''' is a [[derivative (finance)|derivative]] in which the buyer receives payments at the end of each period in which the interest rate exceeds the agreed [[strike price]].  An example of a cap would be an agreement to receive a payment for each month the [[LIBOR]] rate exceeds 2.5%. They are most frequently taken out for periods of between 2 and 5 years, although this can vary considerably.<ref name=":0">{{Cite book|url=https://books.google.com/books?id=iv6_fcBG7YgC|title=Interest-rate Options|last=Coyle|first=Brian|date=2001-01-01|publisher=Global Professional Publishing|isbn=9780852974421|pages=52&ndash;73|language=en}}</ref> Since the strike price reflects the maximum interest rate payable by the purchaser of the cap, it is frequently a whole number integer, for example 5% or 7%.<ref name=":0" /> By comparison the underlying index for a cap is frequently a LIBOR rate, or a national interest rate.<ref name=":0" /> The extent of the cap is known as its notional profile and can change over the lifetime of a cap, for example, to reflect amounts borrowed under an [[amortizing loan]].<ref name=":0" />  The purchase price of a cap is a one-off cost and is known as the premium.<ref name=":0" />

The purchaser of a cap will continue to benefit from any rise in interest rates above the strike price, which makes the cap a popular means of hedging a floating rate loan for an issuer.<ref name=":0" />

The interest rate cap can be analyzed as a series of [[European call option]]s, known as caplets, which exist for each period the cap agreement is in existence. To exercise a cap, its purchaser generally does not have to notify the seller, because the cap will be exercised automatically if the interest rate exceeds the strike (rate).<ref name=":0" /> Note that this automatic exercise feature is different from most other types of options. Each caplet is settled in cash at the end of the period to which it relates.<ref name=":0" />

In mathematical terms, a caplet payoff on a rate ''L'' struck at ''K'' is

:<math> N\cdot \alpha\cdot \max(L-K,0)</math>

where ''N'' is the notional value exchanged and ''<math> \alpha </math>'' is the [[day count fraction]] corresponding to the period to which ''L'' applies. For example, suppose that it is January 2007 now and you own a caplet on the six month [[USD]] LIBOR rate with an expiry of 1 February 2007 struck at 2.5% with a notional of 1 million dollars. Next, if on 1 February the USD LIBOR rate sets at 3%, then you will receive the following payment:

<math>\$1M\cdot 0.5\cdot \max(0.03-0.025, 0) = \$2500</math>

Customarily the payment is made at the end of the rate period, in this case on 1 August 2007.