Calculate the expected 30-day volatility index by interpolating near-term and next-term variance components.
Please enter valid positive numbers. Ensure Next-Term expiry is greater than Near-Term.
Estimated VIX Level0.00
function calculateVIX() {
var sigma1Sq = parseFloat(document.getElementById('nearTermVariance').value);
var sigma2Sq = parseFloat(document.getElementById('nextTermVariance').value);
var t1 = parseFloat(document.getElementById('minutesNear').value);
var t2 = parseFloat(document.getElementById('minutesNext').value);
var errorDiv = document.getElementById('vix-error');
var resultArea = document.getElementById('vix-result-area');
if (isNaN(sigma1Sq) || isNaN(sigma2Sq) || isNaN(t1) || isNaN(t2) || t2 <= t1 || t1 <= 0) {
errorDiv.style.display = 'block';
resultArea.style.display = 'none';
return;
}
errorDiv.style.display = 'none';
// Constants per CBOE Methodology
var N30 = 43200; // Minutes in 30 days
var N365 = 525600; // Minutes in 365 days
// The VIX formula interpolates the two variances to a 30-day (43,200 minute) horizon
// Then takes the square root and multiplies by 100
var term1 = sigma1Sq * t1 * ((t2 – N30) / (t2 – t1));
var term2 = sigma2Sq * t2 * ((N30 – t1) / (t2 – t1));
var interpolatedVariance = (term1 + term2) * (N365 / N30);
var vix = 100 * Math.sqrt(Math.max(0, interpolatedVariance / N365));
document.getElementById('vix-final-value').innerText = vix.toFixed(2);
var interpretation = "";
if (vix = 15 && vix = 25 && vix < 35) {
interpretation = "High volatility: Significant market stress and large price swings expected.";
} else {
interpretation = "Extreme volatility: Market panic or severe crash conditions.";
}
document.getElementById('vix-interpretation').innerText = interpretation;
resultArea.style.display = 'block';
}
Understanding the VIX Calculation Methodology
The CBOE Volatility Index (VIX) is often referred to as the "Fear Gauge." It represents the market's expectation of 30-day forward volatility derived from S&P 500 index options (SPX). Unlike historical volatility, which looks at past price changes, the VIX is forward-looking.
The Core Formula
The mathematical foundation of the VIX is based on a model-independent formula that aggregates the prices of multiple put and call options. The simplified representation used to calculate the variance ($\sigma^2$) for a single term is:
F: Forward index level derived from option prices.
Kᵢ: Strike price of the i-th out-of-the-money option.
Q(Kᵢ): The midpoint of the bid-ask spread for each option.
R: Risk-free interest rate.
Step-by-Step Calculation Process
The actual VIX calculation follows a rigorous four-step process performed in real-time:
Selection of Options: The CBOE selects "Near-Term" (T1) and "Next-Term" (T2) options. These are typically SPX options with expirations between 23 and 37 days.
Calculate Variance for both terms: Using the formula above, the individual variance for the Near-Term and Next-Term is calculated based on the strip of out-of-the-money options.
Interpolation: Since the VIX must represent exactly 30 days of expected volatility, the variances of T1 and T2 are weighted and interpolated to reach a constant 30-day maturity.
The Square Root: The final result is the square root of that 30-day variance, multiplied by 100 to convert it into a percentage-style index value.
Example Scenario
Imagine the Near-Term variance (25 days to expiry) is 0.04 and the Next-Term variance (35 days to expiry) is 0.06. The VIX calculation will weight these two components to find the variance at exactly 30 days. In this simple linear example, the 30-day variance would be roughly 0.05. Taking the square root ($\sqrt{0.05} \approx 0.2236$) and multiplying by 100 gives a VIX level of 22.36.
Why it Matters for Traders
Knowing how the VIX is calculated helps traders understand that it isn't just a random number. It is a direct reflection of the premiums investors are willing to pay for portfolio insurance. When the VIX is high, the cost of options increases because the market anticipates larger price movements (usually to the downside).