Valuing FX Swaps and Forwards with Forward Points
Summary
The document explains an FX swap as an exchange of currencies at spot with a later reversal, and asks how to value the remaining cash flows. Its answer emphasizes that market quotes use forward points: the forward rate is the spot rate plus the quoted points. If an existing trade's agreed points differ from current market points, that difference determines its maturity value; discounting converts it to present value.
The example illustrates a contract that is in the money because its original points are below the current quote, then discounts the resulting currency amount. The same comparison can be applied to an FX forward. The discussion is brief and does not derive a full valuation formula for all cash flows, conventions, currencies, or settlement dates. It also leaves the choice of discount curve and detailed day-count conventions unspecified, so these must be handled consistently in practical pricing.
Key ideas
- FX swap quotes are commonly expressed as forward points relative to the spot exchange rate.
- A forward rate can be represented as spot plus the quoted forward points.
- The difference between contracted and current forward points indicates the trade's value at maturity.
- Present value depends on discounting that maturity amount using relevant interest rates.
- The same quote comparison provides a basis for valuing an existing FX forward.
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Full text
# Valuation of an FX Swap
# 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!
## Answer by Attack68 (score 4)
https://quant.stackexchange.com/a/38959
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.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.