# Valuation of an FX Swap

What is the value of an FX swap? As far as I understand, a typical example of an FX swap would be the following: company A agrees to lend 1000,000.00 euros to B and in exchange B agrees to lend 1000,000.00 x s to A where s is the EUR/USD spot rate which is, say 1.2 and therefore B agrees to lend 1200,000.00 USD to A.

Assume the swap has a maturity of 1 year. In one year, B pays back 1000,000.00*(1+$r_{euro}$) euros to A where $r_{euro}$ is the annual euro interest rate. On the other hand, A has to pay back 1200,000.00*(1+$r_{usd}$) usd to B.

From point of view of A, it has bought a euro bond $B_e$ to B and simultaneously sold a usd bond $B_u$ to B. So does that mean that to value the FX swap, we do: $B_u - B_e$? Now on euro side, A receives from B 1000,000.00 euros. On usd side, we convert the usd payment from A to B which is equal 1200,000.00 x F back to euros, where F is the 1-year forward rate. Hence, the value of the FX swap is 1200,000.00 x F - 1000,000.00 euros or s x (1200,000.00 x F - 1000,000.00) usd?

Similarly for FX Forwards, what would be the time $t$-value of the forward contract?

Thanks!

• You may use latex to make your question more readable. Mar 21, 2018 at 17:41

## 1 Answer

Although FX Swaps are priced via an interest rate parity argument the settlement isn't actually determined by interest rates.

An FX Swap is quoted and specified by something called forward points. If you traded a 1Y EURUSD FX swap at say 140points it means that the forward exchange rate would be .0140 higher (say 1.2140) than the spot FX rate (say 1.2000)

If your specific contract was purchased at say 130points on 1mm EUR notional then it means that you are 10points in the money which corresponds to 1mm * 0.0010 USD = 1000 USD in 1Y time so discounted the value today would be dependent on interest rates, let say the value is 985 USD.

Forward FX Rate = Spot FX Rate + FX Swap Price

So you can effectively use the same principle to value existing forward FX trades.