# Determine forward rates for EUR/USD

I can't wrap my head around how to determine the interest rates to calculate the forward rates of any currency. At this point, I don't even know if this data is actually available to do the calculation myself.

From Investing.com (link) I wish to determine the 1Y and 1M forward rate for starters. I figured out the formula: spot rate x (1 + domestic interest rate) / (1 + foreign interest rate) and I know the spot rate, 1.08 for EUR/USD.

Now when it comes to Domestic and Foreign rates I simply do not understand what I should be using here. First, I figured it must be ESTER and SOFR. The result I get is quite similar but for anything that is not 1Y, any other duration (e.g. 1M) calculation I do just differs greatly. Then I figured Central Bank rates but in the EU it being 0% and in the US 0.5%, that didn't even come near the forward rate.

So now I am confused, how can I calculate these values if that is actually even possible?

• Can you show your calculations?
– fes
Apr 15 at 14:21
• Please take a look here. Apr 15 at 14:49

The ESTR rate should be -0.585 and not 0.585. Converting to monthly form by dividing by 12 and using the CIP formula gives:

$$F=\frac{1+0.0029/12}{1-0.00585/12}\times 1.0810 =1.0818$$

or 8 forward points over the current spot rate. Your website is quoting a market price of roughly 11 forward points. The difference, i.e. the cross currency basis, is merely 3 basis points. For the annual horizon you should be using annual interest rates instead of overnight rates. These are above shorter maturity rates due to expected rate hikes.

• Thank you for your response, this makes sense. Would it be possible to use the treasury rates of each matury and the relevant countries to approximate these forward rates? E.g. use the 1-month bonds from US and Germany to determine EUR/USD 1-month forwards? Apr 19 at 7:22
• @JerBouma I think you could use Treasury rates as well, which should give slightly different results. There is no perfect choice.
– fes
Apr 19 at 7:31

I have a couple of comments to add to your question. First, are you taking into account the time component in your formula? It looks like you're computing the forward rate as

$$S_T = \dfrac{1 + r_d}{1 + r_f} S_0 ,$$ where what it should read is $$S_T = \dfrac{1 + r_d T}{1 + r_f T} S_0 .$$

Moreover, note that this formula assumes that Covered Interest Rate Parity is satisfied, which we know is not the case (as basis are non-zero).

• To determine the 1Y forward rate, I take an ESTER rate of 0.585 and a SOFR rate of 0.290. The spot rate used is 1.081. Plugging this into the formula leads to a value of 247 which is about equal to the 252 Investing.com reports. I make the assumption the rates are annually and thus I don't need to make any time adjustments. I don't mind there being some minor differences as long as it is about the same. When I would like to do this for one month, I set T equal to 1/12 but this does not seem to give me the right answer (25 instead of 11). Apr 15 at 14:46
• I am not sure on how Investing is quoting the exchange rate, but I can't reproduce them if I assume those are basis points using the formula. Maybe because of the basis. Are you plugging $0.585\%$ and $0.290\%$ in the formula or $0.585$ and $0.290$ in the formula? For such small rates I don't think the values for a 1Y FX rate can be so large as compared to the spot. Note that $(1 + 0.585\%) / (1 + 0.290\%) \simeq 1.00294$, i.e. it causes a change of approx $0.3\%$, 30bp as the spot is close to one. Apr 15 at 17:07