What does it mean to find the Present Value of a FRA?

Question

What does it mean when the present value of a forward rate agreement is calculated? Is this a price that the owner of the FRA can sell it for?

Thanks for the help.

Answer 1

At initiation, the value of a FRA is zero. It's computed as the present value of the difference in FRA rates (one entered at time t, the other at time 0).

If you for example entered a 6x9 FRA at a rate of 0.86% and 10 Mio notional at initiation, and the 6 month spot was 0.628%, 9 month 0.712%. If 90 days later, 3m is 1.25% and 6m is 1.35% we have FRA(90,90,90) = FRA on day 90, about to expiry in 90 days with underlying being 90 day libor = ((1.00675/1.003125)-1) * 4 = 1.45%

10000000*((0.0145-0.0086) * (90/360))/(1+0.0135 * (180/360)) = 14651. This is the current market value of the FRA.

Since floating rates rose, the FRA enjoyed a gain.

You can actually approximate this by the rise in the FRA rate by 59bps (145-86) and knowing that 1bp for 90 day and 100000000 notional is 25. Therefore, 10 * 25 * 59= 14750.