FORWARD RATE AGREEMENT

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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.