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A forward rate agreement (FRA) is a contract where the parties agree that an interest rate (contract rate)
will apply to a certain notional principal during a specified future period of time.
An FRA is generally settled in cash at the beginning of the forward period.
This calculator uses simple interest and 30/360 daycount convention.

The price of an FRA can be derived from an arbitrage condition.
At origination, a FRA is priced at the corresponding implied forward rate from today's yield curve.
For example, a "6 X 12" FRA is priced at today's implied six-month forward, six-month interest rate (6R12);
this rate can be calculated using the six-month (0R6) and one-year (0R12) interest rates by solving the following equation.

(1 + 0R6 * .5) * (1 + 6R12 * .5) = (1 + 0R12 *1)

The price of FRAs with different maturities can be calculated by setting up similar equations.
For example, the price of a "3 X 6" FRA can be derived if 0R3 and 0R6 are known,
a "3 X 12" can be priced if 0R3 and 0R12 are know etc.

To value an existing FRA one needs:

  1. Notional principal P
  2. Contract rate C
  3. Forward period t1 to t2
  4. Spot or zero coupon interest rates with maturities t1 and t2 (denoted 0R1 and 0R2, respectively).

Pricing Models Page Available is a Swing Java Jar File if you just wish to run the models.