Interest Rate Cap and Floor - Implied Volatilities

Implied Volatilities

• An important consideration is cap and floor volatilities. Caps consist of caplets with volatilities dependent on the corresponding forward LIBOR rate. But caps can also be represented by a "flat volatility", so the net of the caplets still comes out to be the same. (15%,20%,....,12%) → (16.5%,16.5%,....,16.5%)
  • So one cap can be priced at one vol.

• 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.

• 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.