Interest rate cap and floor

Interest rate caps and interest rate floors Interest rate derivatives are of an optional nature. In an interest rate cap, the buyer will receive at the end of each period in which lies the agreed reference interest rate exceeds the agreed underlying a payment. In an interest rate floor, the buyer will receive at the end of each period in which the agreed reference interest rate is lower than the agreed underlying a payment.

  • 3.1 Black
  • 3.2 Bond Put

Operation

Upon completion of caps or floors in particular the following points should be between the two parties agreed

  • The term of the contract
  • The nominal value of the business
  • The underlying. This is a liquid money market rate in general. Are usual here, for example, for the Euro Euribor and Libor rates for USD.
  • The exercise price. This is called at Caprate Caps and Floors Floor rate.
  • The length of the repricing time periods. The often multi-year duration of the contract is in single interest rate adjustment periods, caplets or floorlets called, divided, usually three to twelve months. Each cap or floorlet is assigned a date and Fixing a date of payment. Usually, the date of the fixing will be a few days before the start of a cap or floorlets and the date of payment of the last day of a cap or floorlets.

Every year on the date of the fixings, the current value of the corresponding money market rate determined (Fixing) and depending on the severity of the caps or floors will determine whether and in what amount payments are made.

The nominal value of the caps or floors is with that Caprate with, called the floor rate with. The observed market interest rate is denoted by, the fraction of the length of the current Interest Period in days and number of days in a year with. The payment of the Caps is that of Floors

Among other things, there are the following forms of caps and floors.

Plain Vanilla

Exceeds the observed money market rate, the cap rate, the cap is charged on the date of payment, the product of the nominal value and the difference between the money market rate and cap rate. Conversely pays a floor, the product of the nominal value and the difference between the floor rate and money market rate.

  • Payoff function cap:
  • Payoff function Floor:

Cap and floor with in arrear Fixing

This expression differs from the plain vanilla expression by the fact that the date of the fixings is not a few days before the beginning of the interest period but a few days before the end of the Interest Period.

Cap Digital and Digital Floor

Exceeds the Fixing the cap rate, the cap is charged regardless of the amount of the excess for a fixed amount. Similarly, in a floor also paid a fixed amount, provided that the fixing was below the floor rate.

Cap and floor with index factor

In addition to the contractually fixed points described above, an index factor is agreed. Exceeds the times of the observed money market rate, the cap rate, the cap is charged on the date of payment, the product of the nominal value and the difference between the times the money market rate and the cap rate. Conversely pays a floor, the product of nominal value and difference of the floor rate and the times the money market rate and money market rate.

  • Payoff function cap:
  • Payoff function Floor:

Collar

A collar is a combination of the payoffs of a cap and a floor. It corresponds with the purchase of a cap and sale of a floor. To the buyer of a collar is thus paid provided that the interest rate fixed higher than the cap rate. If the fixing of the floor rate, so the buyer pays.

  • Payoff function Collar:

Example

Were purchased, for example, interest rate caps for the equivalent of 100,000 Swiss francs with a maximum interest rate of 3.5 % per year and reaches the interest rate applied in the currency Swiss Franc 4% per year, the difference of 0.5 % of the equivalent of is 100,000 (500 francs) per credited year.

With the help of caps the interest rate on a floating rate bond can be fixed up to a maximum. If the maximum amount is exceeded, by the cap, a payoff equal to the difference between the actual interest rate and the upper limit. Also, loans are often sold with a variable interest rate with a cap as a so-called cap - loans.

Similarly, the fixed receiver of an interest rate swap can limit its payments to the top. assessment

The evaluation will be discussed at a Cap. The evaluation of a floor can be derived from this.

A caplet is an option on a swap, a swaption, with only one interest period. Since the individual caplets are independent of each other, each caplet be valued separately. The present value of the cap then the sum of the present values ​​of the individual caplets.

Black

The usual rating for Caps via the model of Fischer Black. Assumption of the model is that the underlying interest rate is log - normally distributed with volatility. In this model, the caplet has to pay a Euribor interest rate which will be fixed at time t and at time T

With

And

Thus, there exists an equivalence relation between the volatility and the present value of the cap. Because all other variables included unstritte values ​​, it therefore makes no difference whether the price of a cap or volatility is called. Accordingly, it is not negotiated in the market about the price of caps and floors, but on the volatility. This Volatitlität is also called Black volatility or implied volatility.

Bond put

It can be shown that a caplet a bond option is similar, so that a review of bond options is possible.

Bondoption John C. Hull
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