Eur/usd Forward Rate Calculation

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EUR/USD Forward Rate Calculator

Current market exchange rate.
Duration of the forward contract.
Annualized interest rate for Euro.
Annualized interest rate for US Dollar.
Calculated Forward Rate: —
Forward Points (Pips): —
Implied Spread: —

Understanding EUR/USD Forward Rate Calculation

The EUR/USD Forward Rate is a financial calculation used by treasurers, investors, and forex traders to determine the exchange rate for a transaction that will occur at a future date (the settlement date). Unlike the "Spot Rate," which is for immediate settlement (usually T+2), the forward rate accounts for the interest rate differential between the Eurozone (EUR) and the United States (USD).

The Interest Rate Parity Formula

This calculator uses the standard Covered Interest Rate Parity (CIRP) formula to determine the fair value of a forward contract. The logic assumes that the return on a dollar asset should equal the return on a euro asset when covered for exchange rate risk.

The formula used is:

F = S × [ (1 + iq × d/360) / (1 + ib × d/360) ]

Where:

  • F = Forward Rate
  • S = Current Spot Rate (EUR/USD)
  • iq = Interest rate of the Quote Currency (USD)
  • ib = Interest rate of the Base Currency (EUR)
  • d = Number of days in the contract (Tenor)
  • 360 = Day count convention (Standard for EUR and USD)

Forward Premium vs. Discount

The relationship between the interest rates determines whether the forward rate trades at a premium or a discount to the spot rate:

  • Premium: If the USD interest rate is higher than the EUR interest rate, the Forward Rate will be higher than the Spot Rate. The market prices in the "cost of carry" to hold the higher-yielding currency.
  • Discount: If the USD interest rate were lower than the EUR interest rate, the Forward Rate would be lower than the Spot Rate.

Example Calculation

Consider a scenario where a corporate treasurer needs to hedge currency risk for 90 days:

  • Spot Rate: 1.1000
  • EUR Rate (Base): 3.00%
  • USD Rate (Quote): 5.00%
  • Tenor: 90 Days

Using the calculator, the Forward Rate would be calculated as roughly 1.1054. This results in +54 pips (Forward Points), indicating the pair is trading at a premium due to the higher USD interest rates.

function calculateForwardRate() { // 1. Retrieve input values var spotRateInput = document.getElementById('spotRate').value; var eurRateInput = document.getElementById('eurRate').value; var usdRateInput = document.getElementById('usdRate').value; var daysInput = document.getElementById('days').value; // 2. Validate inputs if (spotRateInput === "" || eurRateInput === "" || usdRateInput === "" || daysInput === "") { alert("Please fill in all fields (Spot Rate, Interest Rates, and Days)."); return; } var S = parseFloat(spotRateInput); // Spot Rate var r_base = parseFloat(eurRateInput) / 100; // EUR Rate (decimal) var r_quote = parseFloat(usdRateInput) / 100; // USD Rate (decimal) var d = parseFloat(daysInput); // Days if (isNaN(S) || isNaN(r_base) || isNaN(r_quote) || isNaN(d)) { alert("Please enter valid numeric values."); return; } // 3. Define Day Count Convention (Standard FX uses 360 for EUR and USD) var basis = 360; // 4. Calculate Forward Rate using Interest Rate Parity Formula // Formula: F = S * ( (1 + r_quote * (d/360)) / (1 + r_base * (d/360)) ) var numerator = 1 + (r_quote * (d / basis)); var denominator = 1 + (r_base * (d / basis)); var forwardRate = S * (numerator / denominator); // 5. Calculate Forward Points (Pips) // Standard pip for EUR/USD is 0.0001 var spreadRaw = forwardRate – S; var points = spreadRaw * 10000; // 6. Formatting Results // Forward rates are usually quoted to 4 or 5 decimal places var formattedForward = forwardRate.toFixed(4); var formattedPoints = points.toFixed(2); // Determine spread display (Positive or Negative sign) var spreadDisplay = (spreadRaw >= 0 ? "+" : "") + formattedPoints + " pips"; var spreadValueDisplay = (spreadRaw >= 0 ? "+" : "") + spreadRaw.toFixed(5); // 7. Display Results document.getElementById('displayForwardRate').innerHTML = formattedForward; document.getElementById('displayPoints').innerHTML = spreadDisplay; document.getElementById('displaySpread').innerHTML = spreadValueDisplay; // Show the result box document.getElementById('resultBox').style.display = 'block'; }

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