Fair one-year forward for euro versus dollar

Question

You know the current EUR/USD spot rate (dollars per euro) and the one-year interest rates in dollars and in euros. How do you compute the fair one-year forward exchange rate?

Short answer

$F=S\,\tfrac{1+r_{USD}}{1+r_{EUR}}$ (or $Se^{(r_{USD}-r_{EUR})T}$ with continuous rates). Covered interest parity: converting a dollar to euros, investing at the euro rate and converting back forward must give the same as investing at the dollar rate. The higher-yielding currency trades at a forward discount.

Adapted from Joshi, Denson & Downes, Quant Job Interview Questions and Answers, Q2.25, p.18; question and answer rewritten by SelfMadeQuant.com.

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