Valuing FRA

[Marton]

I am struggling to value this FRA “Suppose we entered a receive- floating 6 × 9 FRA at a rate of 0.86%, with notional amount of C$10,000,000 at Time 0. The six- month spot Canadian dollar (C$) Libor was 0.628%, and the nine- month C$ Libor was 0.712%. Also, assume the 6 × 9 FRA rate is quoted in the market at 0.86%. After 90 days have passed, the three- month C$ Libor is 1.25% and the six- month C$ Libor is 1.35%, which we will use as the discount rate to determine the value at g. We have h = 180 and m = 90.”

Assuming the appropriate discount rate is C$ Libor, the value of the original receive- floating 6 × 9 FRA will be closest to:

According to CFI material the answer is

I find this to be a long way of getting the answer, over my entire academic life I have used the formula below to get a value of FRA but in this context it is giving me the wrong answer 14,536 due to rounding

Please tell me what I am missing

[fino_abama]

Value to receive-floating 6 x 9 FRA
= 10,000,000 \times [\frac{1}{1+0.0125 \times (90/360)} - \frac{1 + 0.0086 \times (90/360)}{1 + 0.0135 \times (180/360)}]
= 14,538.93

I would not say your answer is wrong. CFI’s working rounded the FRA(90,90,90) to two decimal places (i.e. 1.45%). If they had used more decimal places (e.g. 1.445483%), then the answer should approach 14,538.94.

[Marton]

Thanks Fino
Much appreciated