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.
Read more about this topic: Interest Rate Cap And Floor
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