# What is the formula for calculating fair value of currency futures?

Let's use AUDUSD 6A futures contract as an example. How does the interest rate between AUD and USD give rise to the fair value calculation of AUDUSD 6A futures contract? Besides interest rates, are there other variables that affect fair value?

• As a first approximation, the future can be treated as a forward, and you can use the familiar relationship between spot price, forward price, and the two interest rates. A more sophisticated approach would have to take into account the varying, random, nature of the interest rates and the correlation between the domestic interest rate (at which the daily m2m of the future can be re-invested) and the spot rate. – Alex C Sep 4 '18 at 1:07

## 1 Answer

$$F = Spot \times e^{(\text{local interest rate} - \text{foreign interest rate}) \times T}$$

where $Spot$ = AUD per dollars.

$T$ is the time to maturity of the contract (in years). So for example if the contract expires in 1 year and a half, $T = 18/12 = 1.5$.

• Thanks. Upvoted. May I ask what exactly is T? I think it's related to time but not sure exactly what it is. Does it change when futures contract is near expiry? – curious Sep 4 '18 at 1:26
• T is the time to maturity of the contract (in years). So for example if the contract expires in 1 year and a half, T = 18/12 = 1.5 – Patriots299 Sep 4 '18 at 1:30
• Thanks. I edited your answer to add this useful information. Marked your answer as the correct one. – curious Sep 4 '18 at 1:37