Select the frequency of the data entered above to calculate annualized volatility correctly.
Number of Observations:0
Period Volatility (Std Dev):0.00%
Annualized Volatility:0.00%
function calculateVolatility() {
var inputStr = document.getElementById("historicalRates").value;
var frequency = parseFloat(document.getElementById("frequency").value);
// Clean and parse input: split by comma, space, newline, pipe, or semicolon
var rawData = inputStr.split(/[\s,\n;|]+/);
var rates = [];
for (var i = 0; i 0) {
rates.push(val);
}
}
var resultBox = document.getElementById("resultBox");
if (rates.length < 2) {
alert("Please enter at least two valid historical exchange rates to calculate volatility.");
resultBox.style.display = "none";
return;
}
// 1. Calculate Logarithmic Returns: ln(Pt / Pt-1)
var logReturns = [];
for (var i = 1; i < rates.length; i++) {
var current = rates[i];
var previous = rates[i-1];
var logRet = Math.log(current / previous);
logReturns.push(logRet);
}
// 2. Calculate Mean of Returns
var sumReturns = 0;
for (var i = 0; i < logReturns.length; i++) {
sumReturns += logReturns[i];
}
var meanReturn = sumReturns / logReturns.length;
// 3. Calculate Variance: Sum((x – mean)^2) / (n – 1)
var sumSquaredDiff = 0;
for (var i = 0; i < logReturns.length; i++) {
var diff = logReturns[i] – meanReturn;
sumSquaredDiff += Math.pow(diff, 2);
}
// Use Sample Variance (n-1)
var variance = sumSquaredDiff / (logReturns.length – 1);
// 4. Calculate Standard Deviation (Period Volatility)
var stdDev = Math.sqrt(variance);
// 5. Calculate Annualized Volatility: StdDev * Sqrt(Frequency)
var annualizedVol = stdDev * Math.sqrt(frequency);
// Formatting results
var displayPeriodVol = (stdDev * 100).toFixed(4) + "%";
var displayAnnualVol = (annualizedVol * 100).toFixed(2) + "%";
// Update DOM
document.getElementById("resCount").innerHTML = rates.length;
document.getElementById("resPeriodVol").innerHTML = displayPeriodVol;
document.getElementById("resAnnualVol").innerHTML = displayAnnualVol;
resultBox.style.display = "block";
}
Understanding Exchange Rate Volatility
Exchange rate volatility is a statistical measure of the dispersion of returns for a given currency pair over a specific period. It is a critical metric for traders, multinational corporations, and risk managers to estimate the potential fluctuation in the value of a currency. High volatility implies a higher risk of large price swings, while low volatility suggests stability.
How to Calculate Historical Volatility
This calculator uses the standard approach for calculating historical volatility based on logarithmic returns. The process involves the following steps:
Collect Historical Rates: Gather a series of closing prices for the currency pair (e.g., EUR/USD) at regular intervals (daily, weekly, etc.).
Calculate Logarithmic Returns: Calculate the natural logarithm of the ratio between consecutive prices.
Rt = ln(Pt / Pt-1)
Calculate Standard Deviation: Compute the standard deviation of these logarithmic returns. This gives the volatility for the specific time period of the data (e.g., daily volatility).
Annualize the Volatility: To make the figure comparable across different assets, volatility is usually annualized by multiplying the period volatility by the square root of the number of periods in a year.
σannual = σperiod × √T
Where T is 252 for daily data (trading days), 52 for weekly, or 12 for monthly.
Example Calculation
Suppose you have the following daily exchange rates for a currency pair:
Day 1: 1.1000
Day 2: 1.1050
Day 3: 1.0980
Day 4: 1.1020
If you input these values into the calculator above with "Daily (252)" frequency, the tool will calculate the log returns between days, find the standard deviation of those returns, and then multiply by the square root of 252 (~15.87) to provide the annualized volatility percentage.
Why Volatility Matters in Forex
Risk Management: Investors use volatility to set Stop Loss and Take Profit levels. A highly volatile pair requires wider stops to avoid being stopped out by market noise.
Option Pricing: Volatility is a primary input in pricing currency options (e.g., using the Black-Scholes model). Higher volatility increases the premium of options.
Hedging Strategies: Companies with foreign exposure use volatility estimates to determine the optimal hedge ratio for their receivables or payables.
Frequently Asked Questions
What is the difference between implied and historical volatility?
Historical Volatility (calculated here) looks backward at past price movements to measure how much the price actually moved. Implied Volatility looks forward and is derived from the market price of options, representing the market's expectation of future volatility.
Why use Logarithmic Returns instead of Simple Returns?
Logarithmic returns are preferred in financial mathematics because they are time-additive and usually follow a normal distribution more closely than simple percentage returns, which is a key assumption in many statistical models.
What is a "normal" volatility for major currency pairs?
Major pairs like EUR/USD or USD/JPY typically show annualized volatility in the range of 5% to 10% during stable periods. However, during economic crises or major geopolitical events, this can spike significantly higher.