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Interest rate cap An interest rate cap is a derivative in which the buyer receives money at the end of each period in which an interest rate exceeds the agreed strike price. An example of a cap would be an agreement to receive money for each month the LIBOR rate exceeds 2.5%. A derivative is a financial contract whose payoffs over time are derived from the performance of assets (such as commodities, shares or bonds), interest rates, exchange rates, or indices (such as a stock market index, consumer price index (CPI) or an index of weather conditions). ...
The strike price, or exercise price, is a key variable in a derivatives contract between two parties. ...
LIBOR stands for the London Interbank Offered Rate and is a daily reference rate based on the interest rates at which banks offer to lend unsecured funds to other banks in the London wholesale (or interbank) money market. ...
The interest rate cap can be analyzed as a series of European call options or caplets which exists for each period the cap agreement is in existence. A call option is a financial contract between two parties, the buyer and the seller of the option. ...
In formulas a caplet payoff on a rate L struck at K is
- Nαmax(L − K,0)
where N is the notional value exchanged and α is the day count fraction corresponding to the period to which L applies. For example suppose you own a caplet on the six month USD LIBOR rate with an expiry of 1st February 2005 struck at 2.5% with a notional of 1 million dollars. Then if the USD LIBOR rate sets at 3% on 1st February you receive 1m*0.5*max(0.03-0.025,0) = $2500. Customarily the payment is made at the end of the rate period, in this case on 1st August工 . In finance, a day count convention is a method to calculate the fraction of a year between two dates. ...
The United States dollar is the official currency of the United States. ...
Interest rate floor An interest rate floor is a series of European put options or "floorlets" on a specified reference rate, usually LIBOR. The buyer of the floor receives money if on the maturity of any of the floorlets, the reference rate fixed below the agreed strike price of the floor. A put option is a financial contract between two parties, the buyer and the seller of the option. ...
A reference rate is any publicly available quoted number or value that is used by the parties to a financial contract. ...
LIBOR stands for the London Interbank Offered Rate and is a daily reference rate based on the interest rates at which banks offer to lend unsecured funds to other banks in the London wholesale (or interbank) money market. ...
The strike price, or exercise price, is a key variable in a derivatives contract between two parties. ...
Valuation of interest rate caps
Black The simplest and most common valuation of interest rate caplets is via the Black model. Under this model we assume that the underlying rate is distributed log-normally with volatility σ. Under this model, a caplet on a LIBOR expiring at t and paying at T has present value The Black model (sometimes known as the Black-76 model) is a variant the Black-Scholes option pricing model. ...
In probability and statistics, the log-normal distribution is the probability distribution of any random variable whose logarithm is normally distributed (the base of the logarithmic function is immaterial in that loga X is normally distributed if and only if logb X is normally distributed). ...
Volatility is the standard deviation of the change in value of a financial instrument with a specific time horizon. ...
- V = P(0,T)(FN(d1) − KN(d2))
where - P(0,T) is today's discount factor for T
- F is the forward price of the rate. For LIBOR rates this is equal to
 - K is the strike
 and In finance, discounting is the process of finding the current value of an amount of cash at some future date, and along with compounding cash form the basis of time value of money calculations. ...
The forward price is the agreed upon price of an asset in a forward contract. ...
 Notice that there is a one-to-one mapping between the volatility and the present value of the option. Because all the other terms arising in the equation are indisputable, there is no ambiguity in quoting the price of a caplet simply by quoting its volatility. This is what happens in the market. The volatility is known as the "Black vol" or implied vol. In financial mathematics, the implied volatility of a financial instrument is the volatility implied by the market price of a derivative based on a theoretical pricing model. ...
As a bond put It can be shown that a cap on a LIBOR from t to T is equivalent to a multiple of a t-maturity put on a T-maturity bond. Thus if we have an interest rate model in which we are able to value bond puts, we can value interest rate caps. Similarly a floor is equivalent to a certain bond call. Several popular short rate models, such as the Hull-White model have this degree of tractability. Thus we can value caps and floors in those models.. In the context of interest rate derivatives, a short rate model is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate. ...
The Hull-White model is a mathematical model of future interest rates. ...
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