# Forward EURUSD exchange rate for a Future date

Assume that on today's date as of 11/22/2020 the 1 year forward exchange rate for EUR/USD is 1.5 for maturity 11/22/2021.

Current RFR for EUR and USD is flat 0.5% and 0.1%.

With this information, can I calculate the expected Forward exchange rate for same maturity for some future date, say 03/22/2021?

• Not without further assumptions. – fesman Nov 22 '20 at 8:25
• So are you looking for the expected value of what the 1 year forward rate will be 03/22/2021 (contract maturing in 03/22/2022)? – fesman Nov 22 '20 at 11:04

I think it's possible. When you say the RFRs are flat, I think we can interpret that as flat for all maturities, including the 1y. So from the 1y Forward rate, we can back out the spot rate via the following relationship between the Spot, Forwards and the RFRs:

$$S_{EUR/USD}(1+r_{USD})^n=(1+r_{EUR}+r_{Basis})^nF_{EUR/USD}$$

Above, $$r_{Basis}$$ stands for the Cross-Currency basis between EUR and USD. In a normal market, you would have the Spot, the Forward, the RFRs, and so the basis term would be the term that you could back out from the equation above.

Given the data you have provided, let's assume that the Xccy basis term is zero. For the 1-year case, $$n=1$$. You can plug in the value for the Forward and the RFRs and back out the spot rate $$S_{EUR/USD}$$.

Then you can plug it back into the equation above again, use the flat RFRs, but adjust the value of $$n$$ to scale it for the maturity you need (so half year would be $$n=0.5$$, two years would be $$n=2$$).

It's only an approximation, but without further info (i.e. the Xccy basis, the full term-structure of the Forwards, etc.) probably as good as we can do.

• Thanks. What other information are required? Why above method is some approximation? – Daniel Nov 22 '20 at 10:24
• What RFRs are we talking about exactly? OIS rates? Zero rates? Normally, you'd take the OIS rates and bootstrap these into zero rates, and then you'd use the zero rates in the equation I wrote. If you assume that the RFRs are OIS fixed swap rates and these are flat for all maturities, then actually the Bootstrapped zero curve is identical to the OIS curve: in that case what I wrote is not an approximation, but an accurate result. – Jan Stuller Nov 22 '20 at 10:54
• What is required here is the term structure of forward points as implied by the term structure of interest rates. Under the assumption that the rates are flat in both currencies (as in your question), you can use Jan’s answer. Of course, as @fesman has stated in their comment, we need more information for a more general answer. – Kermittfrog Nov 22 '20 at 10:55
• Don’t forget the currency basis! – dm63 Nov 22 '20 at 12:13
• @dm63: you're totally right, I've edited the answer. – Jan Stuller Nov 22 '20 at 12:23