A forward rate agreement is an over-the-counter forward contract in which the underlying is an interest rate. FRAs are usually expressed in the “X x Y” convention, ‘X’ represents the point where the underlying loan starts. This also the point where the FRA expires. ‘Y’ represents the point where the underlying loan ends. A 3 x 9 FRA is depicted in the figure below.
The FRA fixed rate i.e. price of an FRA can be calculated using these steps:
The FRA value for pay fixed receive floating can be calculated using these steps:
Example: Suppose we entered a receive-floating 6×9 FRA at a rate of 0.89%, with a notional amount of $5,000,000 at T = 0. After 90 days, the three-month US dollar Libor is 1.10% and the six-month US dollar Libor is 1.25% which will be the discount rate to determine the value. What is the value of the original receive-floating 6×9 FRA?
Solution:
Step 1: Set up the time line.
Step 2: Compute the de-annualized fixed rate:
Step 3: Annualize by multiplying by 360/(n2 – n1)