Realized volatility (RV)
Realized volatility is how much the underlying actually moved over a past window, measured as the standard deviation of its daily log returns and annualized, so it can be compared directly with implied volatility.
From prices to a volatility
Implied volatility is what option prices say the market will do. Realized volatility is what it did. The usual recipe, close to close:
- take a daily closing price for each day of the window;
- turn each pair of closes into a log return, ln(today's close / yesterday's close);
- take the sample standard deviation of those returns (around their mean, dividing by the number of returns minus one);
- multiply by √365 to annualize, and quote it as a percentage.
Log returns add up over time, and a standard deviation of returns scales with the square root of time, which is what makes the annualized figure comparable with an IV.
Why √365
Crypto trades every day, weekends included, so a year has 365 daily returns. Equity markets use about 252 trading days. The convention matters: crypto IVs are annualized over the calendar year too, and theta is per calendar day. The same returns annualized with √252 would read about 17% lower, enough to make options look expensive when they aren't.
A worked example
Six daily BTC closes give five returns:
| Day | Close | Log return | (return − mean)² |
|---|---|---|---|
| 0 | $100,000 | — | — |
| 1 | $102,000 | +1.98% | 1.93 |
| 2 | $99,500 | −2.48% | 9.44 |
| 3 | $101,000 | +1.50% | 0.82 |
| 4 | $104,000 | +2.93% | 5.46 |
| 5 | $103,000 | −0.97% | 2.43 |
The mean return is +0.59% (squared deviations are in percent squared). Their sum is 20.07; divided by 5 − 1 = 4 it gives a variance of 5.02, and its square root is a daily standard deviation of 2.24%. Times √365 ≈ 19.1, that is a realized volatility of about 42.8%. Annualized with √252 instead, the same week would read 35.6%.
Close to close only sees where each day ended. A day that falls 8% in a liquidation cascade and recovers by the close counts as almost no move at all.
Window length
A short window reacts quickly but is noisy: seven returns is a small sample, and one large day dominates it. A 30-day window is steadier but lags a change of regime. Neither is a forecast; both describe the past, which is the comparison implied against realized is built on.
How BOSS computes it
- RV 7d, per venue: seven daily log returns from the last eight completed daily closes at 00:00 UTC of that venue's own reference price (Deribit's perpetual, OKX's spot index, Bybit's spot price), sample standard deviation, times √365. It is recomputed every few hours. All three venues close at the same hour on purpose: in a live check, sampling at a different hour alone moved a 7-day RV by several points.
- RV 30d history: the same formula over rolling 30-return windows of Deribit's perpetual daily closes (Deribit's own days, ending at 08:00 UTC), back to 2021, set against Deribit's DVOL.
Both are on the Dashboard, next to ATM IV over the same horizons.
Live on BOSS
Today's at-the-money implied volatility and 7-day realized volatility on every venue BOSS follows, and Deribit's 30-day realized volatility over time. Look at how much RV swings from month to month; the implied vs. realized article sets it against IV.
| Exchange | ATM IV 7d | ATM IV 30d | RV 7d? | IV 7d − RV 7d | 25Δ put IV | 25Δ call IV |
|---|---|---|---|---|---|---|
| Bybit | 33.5% | 34.8% | 15.4% | +18.1 | 36.5% | 35.2% |
| Deribit | 33.1% | 34.7% | 15.6% | +17.5 | 36.2% | 34.9% |
| OKX | 32.8% | 34.5% | 15.7% | +17.1 | 36.1% | 35.0% |
Realized, 30 days
Common mistakes
- Annualizing crypto returns with √252, which understates realized volatility next to a calendar-year IV.
- Comparing a 7-day RV with a 90-day IV: the windows measure different things.
- Treating a short-window RV as a forecast. Seven returns is a small sample, and one large day can dominate it.
- Forgetting that close-to-close RV misses intraday swings that reverse before the close.
Where this shows up on BOSS
Educational content, not investment advice. See the disclaimer.