# 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