101 Concepts for the Level I Exam

Essential Concept 76: FRA Pricing and Valuation

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:

Set up the time line.
Compute the de-annualized fixed rate: $\frac{\mathrm{1+}\left(\mathrm{r2\times }\frac{\mathrm{n2}}{\mathrm{360}}\right)}{\mathrm{1+}\left(\mathrm{r1\times }\frac{\mathrm{n1}}{\mathrm{360}}\right)}\mathrm{\ -1}$
Annualize by multiplying by 360/(n2 – n1)

The FRA value for pay fixed receive floating can be calculated using these steps:

Find the new FRA fixed rate at time t
Compute payoff at n2: (FRA_t – FRA₀) x (n2 – n1)/360 x NP
Discount back to time t.

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:

We first compute the new FRA rate at time t.

Step 1: Set up the time line.

Step 2: Compute the de-annualized fixed rate:

$\frac{\mathrm{1+}\left(\mathrm{r2\times n2/360}\right)}{\mathrm{1+}\left(\mathrm{r1\times n1/360}\right)}\mathrm{\ -1=\ }\frac{1+\left(0.0125\times \frac{180}{360}\right)}{1+\left(0.0110\times \frac{90}{360}\right)}-1=0.00349$