A volatility quote and a volatility measurement answer different questions. Implied volatility is inferred from option prices for a future horizon; realized volatility is calculated from price changes that already happened. Their difference is useful to study, but it is not a direction signal or a clean forecast error by itself. Cboe’s VIX explainer and the Federal Reserve’s variance-risk-premium research make the forward-looking and realized distinction explicit.
Two clocks, two measurements
Realized variance describes observed movement over a past interval; implied variance is extracted from option prices for a future interval. Realized variance is commonly estimated by summing squared intraperiod returns. Taking its square root puts the result back into volatility units. The Andersen–Bollerslev–Diebold–Labys study develops realized-volatility measurement, while the Federal Reserve’s discussion describes intraday squared returns and option-implied variance as distinct inputs.
The VIX is a familiar illustration, not a universal volatility meter. Cboe calculates it from SPX option quotes to represent option-implied S&P 500 volatility over a constant 30-day horizon; the number conveys expected magnitude, not whether the index will rise or fall. Cboe documents the construction in its VIX explainer, and Robert Whaley’s peer-reviewed VIX analysis explains the index’s interpretation and option-price basis.
What the gap is called—and what it is not
The variance risk premium is defined in asset-pricing theory as the difference between expected variance under risk-neutral pricing and expected variance under the real-world measure. That is a variance comparison, not simply “implied volatility minus realized volatility.” The Federal Reserve paper by Hao Zhou and Yi Zhou sets out that definition and its empirical estimation; Carr and Wu’s published study examines variance risk premia using variance-swap rates and subsequent realized variance.
A practical historical comparison often subtracts the realized variance over a future interval from an option-implied variance observed at the start. That ex-post difference contains both any premium and the gap between the market-implied quantity and the eventual realization. It is therefore a sample statistic, not the premium known with certainty at the start. The Federal Reserve’s measurement discussion and Carr and Wu’s variance-swap framework distinguish expected variance from subsequent realized variance.
Why interpretation needs restraint
Option prices reflect more than a neutral forecast: the risk-neutral and real-world expectations differ by construction, which is the reason a variance-risk-premium concept exists. And an ex-post gap can change with the measurement choices, including how implied variance is estimated and how realized returns are sampled. In its study of stock-market returns, the Federal Reserve reports that its results depend on using model-free implied variance and intraday realized variance; that is evidence about a specified historical design, not a rule that the gap predicts every market or period. See the Federal Reserve study alongside Carr and Wu’s distinct variance-swap study.
How you could test the comparison
Start by fixing the instrument, option horizon, return-sampling method, and variance convention before looking at the result. Record the option-implied measure at the start of each observation window, then calculate realized variance over the same forward horizon from the underlying’s returns. Keep the two series separate before comparing them; do not silently swap volatility for variance or mix calendar and trading horizons. These choices follow the measurement distinctions in the Federal Reserve’s empirical work and its definition of the variance risk premium.
Then preserve the full sequence, including intervals where the comparison does not behave as your hypothesis expects. State whether the test is descriptive or predictive, define the target before inspecting outcomes, and reserve genuinely unseen data for a later check. The backtest acceptance criteria guide explains how to write those decisions down before a curve can persuade you to move them. realbacktesting is a cTrader trading-software studio whose published cBot results are reproducible in the platform; its methodology shows the evidence standard behind those claims.
Takeaway
Implied volatility is a price-derived expectation under a pricing measure; realized volatility is an observation. The gap earns meaning only after you define the units, horizon, and test that produced it.