Implied vs Realized Volatility
Implied volatility (IV) is the volatility input that makes a pricing model output the currently-listed option price; it is forward-looking and reflects the market's priced forecast of future volatility. Realized volatility (RV) is the actual volatility of the underlying computed from historical price moves; it is backward-looking and measures past return dispersion. The persistent gap between them defines the volatility risk premium and is the structural basis for short-volatility strategies.
Side-by-Side
| Property | Implied Volatility (IV) | Realized Volatility (RV) |
|---|---|---|
| Time direction | Forward-looking | Backward-looking |
| Source | Back-solved from current option prices | Computed from historical price series |
| Distribution measure | Risk-neutral | Physical (real-world) |
| Updates | Every option price tick | Periodic (daily, intraday window) |
| Captures event premium | Yes (inflates pre-event, crushes post-event) | No (reflects events only after they realize) |
| Captures jump risk | Yes (priced into wing IV via skew, kurtosis) | Indirectly via historical extremes only |
| Calculation | Numerical inversion of Black-Scholes or model-specific pricing | Standard deviation of log returns over window |
| Time horizon | Implicit in option expiration | User-chosen window (10D, 30D, 60D) |
| Used for | Option pricing, IV rank, IV percentile, hedge sizing | Vol cones, GARCH inputs, VRP analysis |
| Typical relationship | IV > RV by 2-5 vol points (the volatility risk premium) | Lower than IV in steady-state regimes |
When to Use Implied Volatility
- Pricing options. Any option pricing or fair-value calculation uses IV as the input. The IV that prices today's listed option is by definition the IV of that option.
- Hedge sizing. Vega exposure on a portfolio is computed against the IV surface. Position sizing for delta-hedging assumes IV-derived gamma.
- Forward-looking risk assessment. When markets price an event (earnings, FOMC), IV captures the priced uncertainty before the event resolves. RV will only reflect the event after it occurs.
- IV rank and percentile. Strategies that go long volatility when IV is low or short volatility when IV is high need a forward-looking measure. IV rank (current IV relative to its 1-year range) and IV percentile (fraction of time below current IV in the past year) are standard signals.
- Skew and term-structure analysis. The cross-strike and cross-tenor structure of IV reveals priced asymmetries that RV cannot show; the implied distribution at any future date is extractable from the surface.
When to Use Realized Volatility
- Historical regime analysis. Measuring how volatile a stock has actually been over the past N periods. Useful for vol-cone construction and regime change detection.
- VRP measurement. The volatility risk premium is defined as IV minus subsequent RV. Computing VRP requires both an implied measure (current IV) and a realized measure (subsequent RV over the same horizon).
- GARCH-style modeling. Statistical models of vol clustering use historical returns as inputs. RV with appropriate weighting (EWMA, GARCH) provides the empirical basis for forecasting future RV from past RV.
- Backtesting strategies. When evaluating how a strategy would have performed historically, RV is the right measure: it reflects what actually happened, not what the market was pricing.
- Detecting regime breaks. A spike in RV without a corresponding IV expansion (or vice versa) signals that the market is mispricing the regime. This realized-implied divergence is itself a tradable diagnostic.
The Volatility Risk Premium
Implied volatility tends to systematically exceed subsequent realized volatility in equity index options. The gap, measured as IV minus subsequent RV over the same window, is the volatility risk premium (VRP). For SPX, the VRP averages 2-4 vol points across rolling 30-day windows in normal regimes and compresses or inverts during crises.
The VRP is the structural reason short-vol strategies (selling iron condors, short strangles, short variance swaps) earn positive expected returns over time: sellers collect IV premium against subsequent realized vol that comes in lower on average. The risk: when realized exceeds implied, sellers absorb concentrated drawdowns that can erase months of carry in a single regime change. February 2018, March 2020, and August 2024 are recent examples.
Where They Agree
Over long enough windows, average IV across many tickers converges toward average RV plus a stable VRP. The structural relationship (IV = RV + VRP) holds in expectation, even though individual tickers and individual windows show large deviations. Both measures converge on the same underlying quantity (return dispersion) but from different starting points.
For ATM options at the typical 30-DTE horizon in calm regimes, the IV-RV gap is small (1-3 vol points) and the two measures track each other closely. The gap widens at OTM strikes (smile premium that RV cannot capture), at short tenors (jump risk premium), and during regime transitions.
Where They Diverge
- Around binary events. Pre-earnings IV inflates 30-100 vol points above baseline RV; post-event IV crushes back to baseline. RV reflects the event only after it has occurred, by which point IV has already collapsed.
- During regime changes. When a regime is shifting (Aug 2015 yuan devaluation, Feb 2018 vol spike, March 2020 COVID), RV expands faster than IV catches up. Sellers of vol who were short IV against subsequent RV bear the gap.
- For deep OTM strikes. The wing IV (skew, smile) has no RV equivalent; RV measures realized at-the-money returns, not realized tail probabilities. Only the realized frequency of extreme moves over very long windows can validate or invalidate priced wing IV.
- For short-tenor options. 0DTE and weekly options have IV dominated by jump-risk premium; RV computed at standard sampling frequencies cannot capture the same time-scale.
Why They're Often Confused
Both are quoted in vol-point units, both describe "how much the underlying moves," and both feed into option pricing. The crucial distinction is the time direction: IV is what the market is pricing for the future; RV is what already happened. Treating IV as a forecast of RV is roughly correct in expectation but misses the systematic risk premium and the regime-dependent gap structure.
A second source of confusion: IV is reported in annualized form (the standard for option markets), while RV is sometimes reported in raw daily form, requiring users to multiply by sqrt(252) to compare. When using both metrics, ensure both are annualized or both are at the same horizon.
Further Reading
- Live IV vs RV (HV) chart documentation
- Volatility Surface Documentation
- Heston vs Black-Scholes
- What Is Vol of Vol?
- What Is IV Crush?
- Pricing Model Landscape
References
- Carr, P. and Wu, L. (2009). "Variance Risk Premiums." Review of Financial Studies, 22(3), 1311-1341. The seminal empirical work on implied-realized variance gap.
- Bollerslev, T., Tauchen, G., and Zhou, H. (2009). "Expected Stock Returns and Variance Risk Premia." Review of Financial Studies, 22(11), 4463-4492. Connects VRP to expected returns.
- Andersen, T. G., Bollerslev, T., Diebold, F. X., and Labys, P. (2003). "Modeling and Forecasting Realized Volatility." Econometrica, 71(2), 579-625. The reference paper on realized-volatility computation.
- Hull, J. C. (2022). Options, Futures, and Other Derivatives, 11th ed. Pearson. Chapter 15 covers IV computation; Chapter 23 covers historical-volatility estimation.
This is one of the model-vs-model comparison pages. For the full landscape of pricing models and their relationships, see the Pricing Model Landscape.