What is Realized Volatility?
Realized volatility is the actual standard deviation of returns observed over a window — what the market really did, not what options imply it will do.
Definition
Realized volatility (RV) is the historical, observed volatility of a return series — typically annualised. It is computed from the actual price path: take log returns, compute their standard deviation, multiply by √252 (for trading-day annualisation) or √365. RV is the ex-post counterpart of implied vol, and the relationship between them — the volatility risk premium — drives the entire economics of selling options. RV can be measured at different frequencies (daily-close, intraday five-minute, tick) and over different windows (5-day, 20-day, 90-day); each gives a slightly different picture, and the choice depends on what you are using it for.
Why it matters & how it's calculated
The plain-vanilla estimator is the close-to-close estimator: σ̂² = (1/(n−1)) · Σ (rᵢ − r̄)², annualised by √252. But this throws away information available within the day. Better intraday estimators include Parkinson (high-low), Garman-Klass (HLOC), Rogers-Satchell, and Yang-Zhang (which is unbiased to drift and overnight gaps and is the modern desk default for daily-bar RV). For intraday data, the "realized variance" estimator using 5-minute returns and the optimal bias correction for microstructure noise is the standard. The choice matters: in 2024-style low-vol grinding markets, close-to-close RV systematically understates the path-dependent risk a delta-hedged book actually experiences. Vol traders use the spread between intraday RV and close-to-close RV as a signal of "trend persistence" — when intraday RV >> close-to-close, the market is range-bound (good for short gamma); when intraday RV ≈ close-to-close, the market is trending (bad for short gamma).
Formula
σ_RV = √(252) · stdev(ln(Pₜ / Pₜ₋₁)) | Yang-Zhang RV uses open, high, low, close
Worked example
Over the past 20 trading days, SPX daily log returns have a standard deviation of 0.0073. Annualised: 0.0073 × √252 = 0.116 = 11.6% realized vol. Compare that to the 30-day at-the-money IV at 14%. The VRP on the run is 14% − 11.6% = 2.4 vol points — the cushion that systematic vol sellers were earning, before any tail risk.
Related concepts
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