Reading Local and Foreign Rates in FX Forward Valuation

Summary

The document explains which interest rates belong in a currency-pair forward value formula. Its AUD/USD example shows that the quoted price is the value of one Australian dollar expressed in US dollars, so the rate for the quote currency, USD, is applied with a positive sign and the rate for the base currency, AUD, is subtracted. The resulting forward value is spot multiplied by the exponential of the rate difference over time to maturity.

The same convention generalizes to a pair: subtract the base-currency rate from the quote-currency rate. The diagram traces how each currency grows at its own interest rate before taking their ratio, making the sign convention easier to check. This is a concise explanation of the formula rather than a discussion of market conventions, day-count rules, rate curves, compounding choices, or practical pricing adjustments; those details are outside its scope.

Key ideas

• In an AUD/USD quote, the price is expressed in US dollars per Australian dollar.
• The forward value uses the USD rate minus the AUD rate.
• For a currency pair, subtract the base-currency rate from the quote-currency rate.
• The rate difference is applied over the contract's time to maturity.

Tags

# What are "local" and "foreign" interest rate in this formula?


# What are "local" and "foreign" interest rate in this formula?












I found this formula to find fair value of a forex pair:

FV = Spot × e(local interest rate−foreign interest rate) × T

Taken for example AUDUSD,

Spot is AUD per USD.

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.

But, local interest rate and foreign interest rate? Are they respectively AUD(local) and USD(foreign)?

## Answer by Alex C (score 3, accepted)

https://quant.stackexchange.com/a/49910

When in doubt, write down a diagram like this:

```
AUDUSD: price of an AUD measured in USD = 0.68

            Exchange                                Exchange
Country     Today         Interest Rate             in Future
----------  -----         -------------             ---------
USA:        0.68               r_usd     ----->  0.68*exp(r_usd*T)         
Australia:  1.00               r_aud     ----->  1.00*exp(r_aud*T)

Ratio:      0.68                                 0.68*exp((r_usd - r_aud)*T)
```

So the equation is:

$FV_{AUDUSD} = SPOT_{AUDUSD} \times \exp((r_{USD} - r_{AUD})\times T)$

more generally

$FV_{ABCXYZ} = SPOT_{ABCXYZ} \times \exp((r_{XYZ} - r_{ABC})\times T)$

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.