Editing Interest rate cap and floor (section)

==Implied Volatilities==
* An important consideration is cap and floor (so called Black) volatilities. Caps consist of caplets with volatilities dependent on the corresponding forward LIBOR rate. But caps can also be represented by a "flat volatility", a single number which if plugged in the formula for valuing each caplet recovers the price of the cap i.e. the net of the caplets still comes out to be the same. To illustrate: (Black Volatilities) → (Flat Volatilities) : (15%,20%,....,12%) → (16.5%,16.5%,....,16.5%)
** Therefore, one cap can be priced at one vol. This is extremely useful for market practitioners as it reduces greatly the dimensionality of the problem: instead of tracking n caplet Black volatilities, you need to track just one: the flat volatility.
* Another important relationship is that if the fixed swap rate is equal to the strike of the caps and floors, then we have the following [[put–call parity]]: Cap-Floor = Swap.
* Caps and floors have the same implied vol too for a given strike.
** Imagine a cap with 20% vol and floor with 30% vol. Long cap, short floor gives a swap with no vol. Now, interchange the vols. Cap price goes up, floor price goes down. But the net price of the swap is unchanged. So, if a cap has x vol, floor is forced to have x vol else you have arbitrage.
* Assuming rates can't be negative, a Cap at strike 0% equals the price of a floating leg (just as a call at strike 0 is equivalent to holding a stock) regardless of volatility cap.