Forward rate agreement

From Academic Kids


The instruments on which FRAs are based

Before we understand FRAs, we must examine the instruments on which they are based.

- A large international market exists for time deposits issued by large banks in different currencies.
- The Eurodollar deposit is a dollar deposited outside of the U.S. They are the primary time deposit instrument.
- Banks borrow from each other through Eurodollar time deposits, which are short-term unsecured loans.
- Quoted as an add-on yield rather than on a discount basis.

The London Interbank Offer Rate or LIBOR, is the most common rate for borrowing or lending in the Eurodollar/time deposit market. This rate is frequently used in derivative contracts. London banks use LIBOR in their transactions with other banks. LIBOR is typically the rate charged to private, high quality borrowers. Trading in euros/euro deposits occurs in major global cities - 2 rates are used. EuroLIBOR, and Euribor.


In Derivatives Market, a Forward Rate Agreement (FRA) is a forward contract Between two parties to exchange an interest rate differential on a notional principal amount at a given future date (Attention NOT expiration) in which one party, the Long, agrees to Pay a fixed interest payment at a quoted contract rate and Receive a floating interest payment at a reference rate (Underlying rate), determined at Expiration day (Maturity).

Characteristics of forward rate agreements:

  • an forward contract of interest rate.
  • One party makes a fixed interest payment.
  • The other party makes an interest payment based on a referenced rate at the time of contract expiration.
  • The underlying is an interest rate.
  • Payments are based on the difference between the contract rate and the reference rate (e.g., LIBOR).
  • A FRA is a cash-settled forward contract on a short-term loan.
  • The FRA market is not as large as the swaps market.
  • A swap is a special combination of FRAs.

Payoff formula

The FRA payoff formula is: <math> {Payment} = Notional Principal \left( \frac{(Reference Rate-Forward Rate)(Days/360)}{ Reference Rate(Days/360)+1} \right) <math>


  • Notional Principal of the loan,
  • The reference rate is typically Libor or Euribor, also refer as floating rate underlying the agreement.
  • Days is the number of days the loan is for, and
  • Basis is the day count basis applicable to money market transactions in the currency of the loan either 360 or 365 days.
  • (Days/360) is the annualized factor based on 360
  • The numerator is the interest saving in percent, and the denominator is the discount factor.

Note that if the floating rate underlying the agreement turns out to be below the forward rate specified in the contract, the numerator in the formula is negative and the short receives a payment from the long.

FRAs Notation

FRA Descriptive Notation and Interpretation

Notation Contract Expires Settlement Underlying Rate
Expr. x Settlement Starts in A months B months from Now =Settlement Expr.
1 x 3 1 month 3 month 3-1, 60-day LIBOR
1 x 7 1 month 7 7-1, 180-day
3 x 6 3 months 6 6-3, 90-day
3 x 9 3 months 9 9-3, 180-day
6 x 12 6 months 12 12-6, 180-day
12 x 18 12 months 18 18-12, 180-day



See also



External Links


  • Don M Chance, Ph.D., CFA "Analysis of Derivatives for the CFA Program," CFA Institute, pp.34-36
  • Chance, Don M. Analysis of Derivatives for the CFA Program. Charlottesville: Association for Investment Management and Research (2003). This book prepares CFA candidates for taking the exam. Treatment of derivatives is focused strictly on what you need to know to pass the exam. Don't buy it to learn derivatives, because it's not oriented toward a derivatives specialist. But do buy it if you have to pass the CFA exam.

General areas of finance

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Financial markets | Fund management | Financial institutions | Personal finance | Public finance | Financial mathematics | Financial economics
ru:Соглашение о будущей процентной ставке (FRA)



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