What Is Realized Volatility?

Last reviewed: May 17, 2026 by Options Analysis Suite Research.

What Is Realized Volatility?

Realized vol takes a sequence of historical returns and computes the sample standard deviation. The calculation differs depending on the input data and the estimator. The simplest is close-to-close:

RV_close = sqrt( (1/(n-1)) * sum_i (r_i - r_bar)^2 ) * sqrt(252)

where r_i is the daily log return and 252 is the annualization factor for trading days. This is the most common metric retail traders see, but it is statistically inefficient because it discards intraday range information.

What Are the Major Realized-Volatility Estimators?

• Close-to-close. Simplest. Uses only daily closing prices. High variance estimator, especially on noisy assets.
• Parkinson (1980). Uses the daily high-low range. Roughly five times more efficient than close-to-close for diffusion-only processes. Formula: RV_park = sqrt( (1 / (4*ln 2)) * (1/n) * sum_i (ln(H_i / L_i))^2 ) * sqrt(252). Limitation: ignores opening jumps; biased downward when overnight returns dominate.
• Garman-Klass (1980). Uses open, high, low, close. Variance reduction roughly 7-8x over close-to-close. Combines range information with squared open-close.
• Rogers-Satchell (1991). Robust to drift in the underlying. Uses open, high, low, close with a drift-independent formula. Useful when the asset has nonzero average return over the sample.
• Yang-Zhang (2000). Combines Garman-Klass with explicit handling of overnight returns. The most efficient simple estimator: roughly 14x variance reduction over close-to-close for typical equity data. Industry standard for daily-frequency RV estimation.
• Realized variance from intraday returns. Andersen-Bollerslev-Diebold-Labys (2003): sum of squared 5-minute (or higher-frequency) returns. Approximates the integrated variance under continuous-time models. Sensitive to microstructure noise; jump-robust extensions (bipower variation, two-scale RV) handle the noise.

Sampling Frequency Tradeoffs

• Higher frequency = more efficient under diffusion. Theoretically, sampling at every microsecond converges to the true integrated variance. In practice, microstructure noise (bid-ask bounce, discrete tick sizes, latency) dominates at very high frequencies.
• Optimal sampling. Empirical studies (Aït-Sahalia-Mykland-Zhang 2005) suggest 5-minute sampling is the practical sweet spot for liquid US equities and indices. For less-liquid single names, 15- or 30-minute sampling reduces noise.
• Window length. 10-day RV captures recent vol; 30-day RV is the standard reference matching VIX. 90-day RV smooths but lags. The choice depends on whether you want responsiveness or stability.

RV vs IV

The persistent gap between implied vol (priced today) and subsequently realized vol (measured ex post) is the variance risk premium. Three empirical regularities:

• IV exceeds RV on average across SPX history (~2-4 vol points).
• Hit rate (% of windows IV > RV): approximately 70%.
• The gap compresses or inverts during volatility spikes when realized vol catches up to elevated IV.

This gap is the structural reason short-vol strategies generate positive carry, and the reason long-vol hedges have negative carry on average.

Worked Example

SPY trailing 30-day RV across estimators on a representative date:

• Close-to-close: 11.8%
• Parkinson: 10.5%
• Garman-Klass: 10.2%
• Yang-Zhang: 10.4%
• Realized variance (5-min): 11.0%
• VIX (priced 30-day IV): 14.5%

The 4-vol-point gap between VIX and RV measurements is consistent with historical equity VRP. Yang-Zhang and 5-min RV converge closely; close-to-close is biased upward because of overnight gap variance.

How Do Pricing Models Use RV?

• Black-Scholes: the canonical model assumes constant sigma. Historical RV is one estimate of sigma; calibrated implied IV is another. The two diverge because the assumption of constant vol is empirically false.
• Heston: the Heston variance state v_t plus integrated variance over [t, T] connect to the RV that would be observed over [t, T] under the model dynamics. Calibrating to surface IVs and comparing the implied integrated variance to subsequent realized variance is a Heston validation test.
• Jump diffusion: jumps add variance. RV decompositions (Barndorff-Nielsen-Shephard 2004) separate diffusive RV from jump-RV using bipower variation, an important diagnostic for jump-augmented models.

RV in Trading Applications

• IV Rank and IV Percentile. Comparing today's IV to the trailing distribution of IV is one form of normalization; comparing IV to current RV is another. Both are useful, neither is sufficient on its own.
• Variance swap mark-to-market. A live variance swap's P&L is the difference between the floating-leg accumulated realized variance and the fixed-leg variance strike. Realized variance is the literal payoff measurement.
• Volatility forecasting. RV is the input to GARCH and HAR-RV forecasting models. Forecasting next-period RV is a separate problem from measuring past RV.
• Greek-aware position sizing. Selling vol when RV is low and IV is high is the canonical short-vol setup; the IV-RV gap is the priced premium being harvested.

Limitations and Caveats

• RV is backward-looking. It tells you what happened, not what will happen. Forecasting next-period RV is a separate task.
• Estimator bias near jumps. Standard estimators conflate jump-variance with diffusion-variance. Jump-aware estimators (bipower variation, threshold methods) separate the two.
• Microstructure noise at high frequencies. Sampling at 1-second or finer introduces bias from bid-ask bounce. Robust estimators (two-scale, multi-scale, kernel) correct for this.
• Drift contamination. Long-window estimators that don't subtract the mean return are biased when the underlying has drift. Most implementations subtract the mean implicitly.

Related Concepts

Variance Risk Premium · IV vs HV History · VIX · Implied Volatility · Heston Model · Term Structure · Pricing Model Landscape

References & Further Reading

• Parkinson, M. (1980). "The Extreme Value Method for Estimating the Variance of the Rate of Return." Journal of Business, 53(1), 61-65. The first range-based volatility estimator.
• Garman, M. B. and Klass, M. J. (1980). "On the Estimation of Security Price Volatilities from Historical Data." Journal of Business, 53(1), 67-78. The OHLC estimator.
• Rogers, L. C. G. and Satchell, S. E. (1991). "Estimating Variance from High, Low and Closing Prices." Annals of Applied Probability, 1(4), 504-512. Drift-robust range estimator.
• Yang, D. and Zhang, Q. (2000). "Drift-Independent Volatility Estimation Based on High, Low, Open, and Close Prices." Journal of Business, 73(3), 477-491. The Yang-Zhang estimator.
• Andersen, T. G., Bollerslev, T., Diebold, F. X. and Labys, P. (2003). "Modeling and Forecasting Realized Volatility." Econometrica, 71(2), 579-625. Realized volatility from intraday data.

View live SPY IV vs HV across estimators ->

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