An interest-rate cap is an OTC derivative that protects the holder from rises in short-term interest rates by making a payment to the holder when an underlying interest rate (the “index” or “reference” interest rate) exceeds a specified strike rate (the “cap rate”). Caps are purchased for a premium and typically have expirations between 1 and 7 years. They may make payments to the holder on a monthly, quarterly or semiannual basis, with the period generally set equal to the maturity of the index interest rate.

Each period, the payment is determined by comparing the current level of the index interest rate with the cap rate. If the index rate exceeds the cap rate, the payment is based upon the difference between the two rates, the length of the period, and the contract’s notional amount. If the index rate does not exceed the cap rate, no payment is made for that period.

If a payment is due on a USD Libor cap, it is calculated as

[1]

For example, Exhibit 1 illustrates a 3-year, USD 200MM notional cap with 6-month Libor as its index rate, struck at 3.5%. The exhibit shows what the cap’s payments would be under a hypothetical interest rate scenario.

Exhibit 1: Payments made under a hypothetical interest rate scenario by a 3-year USD 200MM notional cap linked to 6-month USD Libor with strike rate of 3.5%. Values for the index rate are 2.15%, 3.75%, 2.75%, 4.50%, 4.00%, and 3.25%. These result in payments of USD 0MM, USD .25MM, USD 0MM, USD 1MM, USD .5MM, and USD 0MM.

Exhibit 1: Payments made under a hypothetical interest rate scenario by a 3-year USD 200MM notional cap linked to 6-month USD Libor with strike rate of 3.5%. Values for the index rate are 2.15%, 3.75%, 2.75%, 4.50%, 4.00%, and 3.20%. These result in payments of USD 0MM, USD .25MM, USD 0MM, USD 1MM, USD .5MM, and USD 0MM.

Caps are frequently purchased by issuers of floating rate debt who wish to protect themselves from the increased financing costs that would result from a rise in interest rates. To reduce the up-front cost of such protection, a long cap may be combined with a short floor to form a collar.

A cap can be thought of as a series of interest rate options called caplets. Caps are priced by valuing the individual caplets and summing the values. The Black ’76 option pricing formula is the market convention for quoting implied volatilities for caps.

Caps are usually quoted with an up-front premium. If they are quoted with an implied volatility, it is with a flat implied volatility across all caplets.

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