Fx Spot Rate Calculation

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Implied FX Spot Rate Calculator

Calculate the theoretical Spot Rate based on Forward Rates and Interest Rate Parity

The agreed rate for future delivery
Duration of the forward contract
Annual rate for the first currency in pair (e.g., EUR in EUR/USD)
Annual rate for the second currency in pair (e.g., USD in EUR/USD)
ACT/360 (Standard for most currencies) ACT/365 (GBP, HKD, etc.)
Implied Spot Rate: –
Forward Points Difference: –
Base Currency Factor: –
Quote Currency Factor: –

About FX Spot Rate Calculation

The FX Spot Rate represents the current market price for exchanging one currency for another for immediate delivery (typically T+2 days). While spot rates are usually determined by market supply and demand, they are mathematically linked to Forward Rates through the concept of Interest Rate Parity (IRP).

This calculator determines the Implied Spot Rate by working backward from a known Forward Rate and the interest rate differential between the two currencies. This is crucial for traders analyzing whether a forward contract is priced fairly relative to interest rate expectations.

The Formula

The calculation uses the rearranged Interest Rate Parity formula:

Spot = Forward × [ (1 + R_base × T/Basis) / (1 + R_quote × T/Basis) ]

  • Forward: The exchange rate for future delivery.
  • R_base: Annual interest rate of the Base currency (decimal).
  • R_quote: Annual interest rate of the Quote currency (decimal).
  • T: Time to maturity in days.
  • Basis: Day count convention (usually 360 or 365).

Calculation Example

Imagine you have a Forward Rate for EUR/USD of 1.1200 for a 90-day period.

  • Base Currency (EUR) Interest Rate: 3.0%
  • Quote Currency (USD) Interest Rate: 5.0%
  • Basis: 360 days

To find the Spot Rate required to justify this Forward Rate:

1. Base Factor = 1 + (0.03 × 90/360) = 1.0075
2. Quote Factor = 1 + (0.05 × 90/360) = 1.0125
3. Spot = 1.1200 × (1.0075 / 1.0125) ≈ 1.1145

In this scenario, the Spot Rate is approximately 1.1145.

function calculateFXSpot() { // 1. Get input values var forwardRateInput = document.getElementById('forwardRate').value; var timeDaysInput = document.getElementById('timeDays').value; var baseIntRateInput = document.getElementById('baseIntRate').value; var quoteIntRateInput = document.getElementById('quoteIntRate').value; var dayBasisInput = document.getElementById('dayCountBasis').value; // 2. Validate inputs if (forwardRateInput === "" || timeDaysInput === "" || baseIntRateInput === "" || quoteIntRateInput === "") { alert("Please fill in all fields to calculate the spot rate."); return; } var F = parseFloat(forwardRateInput); var T = parseFloat(timeDaysInput); var Rb = parseFloat(baseIntRateInput) / 100; // Convert percentage to decimal var Rq = parseFloat(quoteIntRateInput) / 100; // Convert percentage to decimal var Basis = parseFloat(dayBasisInput); if (isNaN(F) || isNaN(T) || isNaN(Rb) || isNaN(Rq) || isNaN(Basis)) { alert("Please enter valid numeric values."); return; } if (Basis === 0) { alert("Basis cannot be zero."); return; } // 3. Perform Calculation // Formula: Spot = Forward * ( (1 + Rb * T/Basis) / (1 + Rq * T/Basis) ) // Note: Standard Forward Rate Formula is F = S * ( (1 + Rq*T/Basis) / (1 + Rb*T/Basis) ) // Therefore, solving for S (Spot) reverses the fraction. var timeFactor = T / Basis; var baseFactor = 1 + (Rb * timeFactor); var quoteFactor = 1 + (Rq * timeFactor); var spotRate = F * (baseFactor / quoteFactor); var pointsDiff = F – spotRate; // 4. Display Results // Determine decimal precision based on input. Usually FX is 4 or 5 decimal places. // We will default to 5 decimal places for precision. document.getElementById('displaySpotRate').innerHTML = spotRate.toFixed(5); document.getElementById('displayPoints').innerHTML = (pointsDiff * 10000).toFixed(2) + " pips (" + pointsDiff.toFixed(5) + ")"; document.getElementById('displayBaseFactor').innerHTML = baseFactor.toFixed(6); document.getElementById('displayQuoteFactor').innerHTML = quoteFactor.toFixed(6); // Show result box document.getElementById('resultBox').style.display = 'block'; }

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