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Understanding Currency Spot Rate Calculation
The Currency Spot Rate is the current price at which a particular currency pair can be bought or sold for immediate delivery. While spot rates are typically observed directly in the Forex market, calculating the theoretical spot rate is a critical task in financial engineering, particularly when dealing with derivatives like forwards and futures.
Spot Rate vs. Forward Rate
The relationship between the Spot Rate and the Forward Rate is governed by the principle of Covered Interest Rate Parity (CIRP). This economic theory states that the difference between the forward and spot exchange rates implies the interest rate differential between the two currencies. If this were not true, arbitrageurs could make risk-free profits.
Our calculator allows you to reverse-engineer the Spot Rate if you know the Forward Rate and the respective interest rates of the two currencies involved. This is useful for:
- Verifying market pricing consistency.
- Determining the no-arbitrage price of a currency pair.
- Academic and financial modeling purposes.
The Calculation Formula
To calculate the Spot Rate ($S$) from a Forward Rate ($F$), we rearrange the standard Forward Rate formula:
$$ S = F \times \frac{1 + (r_{base} \times \frac{d}{B})}{1 + (r_{price} \times \frac{d}{B})} $$
Where:
- S = Spot Exchange Rate
- F = Forward Exchange Rate
- rbase = Interest rate of the Base Currency (decimal)
- rprice = Interest rate of the Price (Quote) Currency (decimal)
- d = Number of days to maturity
- B = Day count basis (usually 360 or 365)
Example Calculation
Imagine you have a Forward Rate for EUR/USD of 1.1200 maturing in 90 days.
- Base Currency (EUR) Rate: 3.00%
- Price Currency (USD) Rate: 5.00%
- Basis: 360 days
First, calculate the time factors:
Time Factor = 90 / 360 = 0.25
Then apply the interest adjustment:
Base Factor = 1 + (0.03 × 0.25) = 1.0075
Price Factor = 1 + (0.05 × 0.25) = 1.0125
Finally, solve for Spot:
S = 1.1200 × (1.0075 / 1.0125) ≈ 1.1145
In this scenario, the Spot Rate is approximately 1.1145. The Forward Rate is higher than the Spot Rate because the Price Currency (USD) has a higher interest rate than the Base Currency (EUR), creating a forward premium/discount dynamic.
Key Definitions
Base Currency: The first currency in a pair (e.g., EUR in EUR/USD). The exchange rate represents how much of the second currency is needed to buy one unit of the base currency.
Price (Quote) Currency: The second currency in a pair (e.g., USD in EUR/USD).
Swap Points: The difference between the Forward Rate and the Spot Rate, typically quoted in "pips".
function calculateSpotRate() {
// Get inputs using var
var forwardInput = document.getElementById("forwardRate");
var daysInput = document.getElementById("daysToMaturity");
var baseRateInput = document.getElementById("baseInterestRate");
var priceRateInput = document.getElementById("priceInterestRate");
var basisSelect = document.getElementById("dayCountConvention");
// Parse values
var F = parseFloat(forwardInput.value);
var t = parseFloat(daysInput.value);
var rBase = parseFloat(baseRateInput.value);
var rPrice = parseFloat(priceRateInput.value);
var basis = parseFloat(basisSelect.value);
// Validation
if (isNaN(F) || isNaN(t) || isNaN(rBase) || isNaN(rPrice) || F <= 0 || t = 0 ? "+" : "") + swapDiff.toFixed(5);
}