# What are “local” and “foreign” interest rate in this formula? [closed]

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)?

• Hello Gio and welcome to SE. Try to think in terms of two equivalent operations: 1. putting the money in a USD-denominated bank account, then exchanging to AUD 2. exchanging to AUD and then putting the money in a AUD-denominated bank account. Thanks – byouness Nov 25 '19 at 15:50

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

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

• Another way to remember it is "The high interest rate currency is seen to depreciate in the forward market from the point of view of the other currency". Then you can write down the equation directly. No need for a diagram. – Alex C Nov 25 '19 at 18:14
• Thank you. I found right now an equation to find fair value of a stock: FV = Stock [1 + (Interest - Dividend)]. Is it an equivalent equation to the one of my question? – Gio Nov 25 '19 at 23:29
• FV is not "fair value", but forward value, the price you agree now for delivery in the future. Just like there are currency forwards, there are also stock forward contracts (although not very common). Indeed the principles are the same, interest is analogous to domestic interest rate and dividend to 'foreign' interest rate. – Alex C Nov 25 '19 at 23:33