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Interest Rate Parity and Currency Futures Fair Value

Article Quant Q&A · Author: curious
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Summary

The document gives a basic cost-of-carry expression for the fair value of an AUD/USD currency futures contract. It relates the futures price to spot and the difference between the local and foreign interest rates, compounded continuously over the time remaining to maturity. The example defines maturity in years, illustrating how a contract with a stated number of months is converted into a year fraction before applying the rate differential.

This is a concise answer to how interest rates enter the calculation, but it does not address the question’s broader request about other variables that may affect fair value. It also supplies no assumptions about borrowing and lending rates, transaction costs, market conventions, or collateral, and gives no numerical inputs or worked price calculation. The quoted relationship is therefore a baseline parity formula; practical valuation may require conventions and adjustments not discussed in the document.

Key ideas

  • Currency futures fair value is linked to spot through the interest rate differential between the two currencies.
  • The rate difference is applied over the time to maturity using continuous compounding.
  • Maturity should be expressed as a year fraction in the stated formula.
  • The answer does not discuss additional market variables or practical valuation adjustments.

Tags

ForexFuturesDerivatives pricingCarry
Full text
# What is the formula for calculating fair value of currency futures?


# 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?

## Answer by Patriots299 (score 6, accepted)

https://quant.stackexchange.com/a/41566

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

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, $T = 18/12 = 1.5$.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.