Realised vs Implied Volatility Explained
Realised volatility is calculated from observed price returns over a past period, whereas implied volatility is inferred from options prices under a pricing framework. Both are conventionally annualised, but they answer different questions. A high implied-volatility number is not a guarantee that realised market movements will be large, and the difference is not a risk-free trading opportunity.
What realised volatility measures
Historical or realised volatility commonly estimates the standard deviation of a sequence of returns, sometimes using log returns. It depends on observation frequency, sample size and the chosen estimator. Daily closing-to-closing returns miss some intraday price movements; high-low range estimators use different information. A result calculated from one month of daily returns should not automatically be compared with a long-run annual measure without converting units and acknowledging sampling uncertainty.
A worked annualisation example
Suppose fictional daily returns have sample standard deviation 1.2%. Using a common equity-market assumption of 252 trading days, annualised realised volatility is 1.2% × square root of 252 ≈ 19.05%. The scaling relies on assumptions about return dependence and stable variance. A market with volatility clustering, jumps or changing trading hours may not obey simple square-root-of-time scaling exactly.
What option-implied volatility represents
A model can infer the volatility input that makes its calculated option price match a market quotation. That input is called implied volatility. It reflects option pricing, interest rates, dividends, strike, maturity and other assumptions—not necessarily a neutral best estimate of future statistical volatility. Different strikes and maturities often have different implied values, producing a volatility smile or skew.
Why implied and realised numbers differ
Investors may pay for downside protection, and sellers may require compensation for bearing sharp moves or providing scarce liquidity. These effects can cause implied volatility to exceed subsequently observed volatility on average in some markets and periods. But there are episodes when realised moves far exceed what was implied, inflicting large losses on short-option positions. No historical average spread guarantees a future premium.
Worked comparison for an option horizon
Suppose 30-day at-the-money implied volatility is 24% annualised, while trailing realised volatility annualised from daily returns is 17%. The simple difference is 7 percentage points. It would be incorrect to call that a 7% assured profit from selling options. The measures refer to different horizons or estimation windows, and option returns depend on skew, gamma, vega, price direction, hedging, transaction costs and extreme outcomes.
Why VIX is related but not identical
VIX is an index derived from a basket of S&P 500 options to estimate a form of 30-day implied variance, and is often quoted as annualised volatility. It is not just the Black–Scholes implied volatility of one at-the-money option. Changes in option demand can alter VIX even without a corresponding realised move in the cash index. Other assets have distinct volatility surfaces and benchmark conventions.
Volatility regimes and forecasting limitations
Volatility often clusters: turbulent sessions can be followed by further turbulence. Models such as EWMA and GARCH attempt to incorporate this property, but their predictions depend on calibration and may break during structural shocks. Realised volatility calculated after the fact cannot be used as though known at the start of a backtest interval. Preserve data timestamps when evaluating strategies.
A practical comparison framework
Match underlying asset, currency, horizon, return convention and date. Compare realised-volatility windows with the option’s remaining maturity and examine how implied volatility differs across strikes. Record liquidity, option bid–ask spreads and major events. When illustrating option payoffs, test price jumps and scenario changes rather than extrapolating an average implied–realised difference.
Illustrated volatility difference: implied versus realised
Hypothetical annualised percentages over different measurement windows; comparison is educational, not an option-return forecast.
Illustrative values only; see the explanation below for assumptions and limitations.
The seven-percentage-point gap is not a seven-percent guaranteed return. One statistic summarises historical movements while the other is inferred from market option prices for a future maturity under a chosen methodology. A fair comparison should match underlying, horizon and calendar convention and should consider the full options volatility surface, including strike. In a sudden market shock, realised moves can substantially exceed earlier implied figures. Option-selling losses can be far greater than their collected premium.
Related educational material: volatility and changing market risk regimes.
How to compare realised and implied volatility on the same horizon
Suppose daily percentage returns over a defined historical sample have a standard deviation of 1.00%. A common approximation annualises this daily dispersion by multiplying by the square root of 252 assumed trading days, giving approximately 15.87% annualised realised volatility. This is a historical estimate; it depends on the sampled dates, return calculation, data quality, choice of annualisation convention and the assumption that the square-root-of-time scaling is informative.
Now suppose an at-the-money option market implies 22% annualised volatility over a roughly one-month horizon. Simply comparing 22% implied with 15.87% realised does not show the options are overpriced. The two figures relate to different time windows: one is a market-implied parameter for a future option horizon, while the other summarises past realised price variation. Forward event risk, volatility risk premia and model assumptions matter. The option price also responds to rates, dividends, strike, maturity and the volatility smile.
| Metric | Example | Interpretation |
|---|---|---|
| Historical daily return dispersion | 1.00% | Observed sample variation |
| Annualised historical estimate | 1% × √252 ≈ 15.87% | Scaled realised estimate |
| Illustrative option-implied measure | 22% annualised | Market-implied future-horizon parameter |
Why the common ‘expected move’ shortcut has limits
A rough market convention multiplies annualised implied volatility by the square root of the fraction of a year remaining. For example, 20% annualised volatility over 30 calendar days gives 0.20 × √(30/365) ≈ 5.73%. This scale can help frame a one-standard-deviation-style move under simplified distributional and modelling assumptions; it is not a guaranteed trading range, a directional forecast or an exact probability interval. Options can price skewed and fat-tailed risks that this one-number approximation conceals.
Compare the same underlying instrument, comparable return conventions, consistent dates and a clearly defined historical window versus future expiry. For research around equity-index options, consult Cboe’s VIX methodology resources; for a related but different historical-volatility measure, see Average True Range Explained. VIX is itself calculated from option prices and should not be equated with a simple realised-volatility average.
Frequently asked questions
Is implied volatility a forecast of stock direction?
No. It relates to option-implied dispersion, not whether a stock will rise or fall.
Can realised volatility exceed implied volatility?
Yes, especially during unexpected market shocks.
Does annualised 20% volatility mean a 20% fall is expected?
No. It is a dispersion measure and does not establish direction or a guaranteed range.
Sources and further reading
Related learning: VIX Explained: Expected Volatility and Limitations.