Cap Floor Volatility

This is an iterative process to obtain caplet volatility based on cap volatility.

Cap floor volatility.

10 spot rate 8 strike 2. The implied caplet volatility using normal formula. Sum of the fair values of the caplets. Aarcap cm bl dgen tables d v d e d m d f cpn d l cpn freq eff mktdays npa rate ex vol corr tbl r table r option type set pay scalefactor acc cm acc pay hl d rul pay freq cm numcf cm yld d rul cm df crv acc df crv disc.

Caps consist of caplets with volatilities dependent on the corresponding forward libor rate. In other words cap floor swap. Once we have floors correctly valued we will implement volatility stripping. When comparing to other vanilla derivatives cap and floor pricing offers an additional complexity as it does not involve a single volatility number.

If the implied volatility is calculated assuming that all the caplets have the same volatility then the resulting. Calculates implied volatility spread for a generic cms cap floor using the black model dates generated. The volatility used in valuing each caplet using the black model is called the spot volatility and is the volatility of the forward rate. From the pricing examples above we see that this value is.

We start from the model that banco popular proposed and develop different models to improve the results. So let us start with writing the cap floor parity. The mechanisms are the same as above. At the money forward to be more precise is the one giving you the same price for call and put or in this case the same price for cap and floor.

Cap k floor k swap k where swap k is a swap paying k and that has the exact same characteristics maturity schedule etc as the cap and floor. 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. We can compute the implied caplet volatility using linear exponential quadratic models in the same way we can compute the prices of a caplet ting the flat volatility or other parameters. The cap floor parity says that being long a cap and short a floor with the same strike is equivalent to paying the fixed leg in the swap where the fixed rate is equal to the strike rate.

This process could end up in a sharp volatility surface that will be unrealistic on financial markets so some methods will be discussed to smooth it. If libor 3 month is 10 the borrower pays only the strike 8 and the seller of cap pays the difference. If libor 3 month becomes 6 the borrower pays only 6. The strike is 8.

The atm level atmf. Indeed a cap floor can be broken down into a strip of forward starting options over a floating rate and each one of these options called caplet floorlet should be priced with a different volatility. The net of the caplets still comes out to be the same.