The VIX Calculation Explained Without the Marketing

The VIX is the square root of a 30-day variance swap rate computed from live SPX option prices, a replicated price rather than a forecast.

The VIX is not a forecast of future volatility. It is the square root of the fair strike of a 30-day variance swap on the S&P 500, annualised, computed directly from the live prices of a strip of out-of-the-money SPX options rather than from any statistical model of what volatility will do next. Calling it a fear gauge obscures the fact that it is model-free replication, the same construction covered in variance swaps and how they are replicated, applied to a rolling window pinned at 30 days.

The CBOE formula sums the mid-quote price of every out-of-the-money SPX put and call across the available strikes, weights each one by the width of the strike interval around it divided by the square of that strike, and scales the total by two divided by time to expiry in years. Subtracting a small correction term tied to the forward price and the at-the-money strike removes residual sensitivity to the exact forward level, leaving a number that is the fair variance of a 30-day variance swap under the replication logic set out above. Taking the square root of that variance and multiplying by 100 turns it into the volatility points quoted on screen.

Because the calculation prices a strip of options that already trade, the resulting number is the market’s current price of 30-day variance, set under the same risk-neutral measure that prices every other option, not a statistical projection built from historical returns. That distinction matters because the risk-neutral price of variance carries the variance risk premium described in the pricing of every option that feeds into it, so the index sits, on average, above the volatility that subsequently occurs, in the same way a single option’s implied volatility tends to run above the realised volatility of its underlying.

SPX options do not expire in exactly 30 days on any given trading day, so the calculation blends two expiries, the nearest one with more than 23 days to run and the next one out, weighting each by how close its own time to expiry is to the 30-day target. This interpolation keeps the published index pinned to a constant 30-calendar-day horizon every trading day, rather than letting the effective horizon shrink toward zero as a single listed expiry approaches, which would make the index level jump mechanically every time the front contract rolled.

If the weighted strip on a given day prices a variance of 256, the square root is 16, and the index prints at 16.00, read as an annualised 16 percent standard deviation of S&P 500 returns priced over the coming 30 days. Dividing that level by the square root of 252, roughly 15.9, converts it to an implied daily standard deviation of close to 1 percent, a conversion desks use constantly to translate the headline number into the size of daily move the market is currently pricing.