Historical (realized) volatility

简要解答

Historical volatility — also called realized volatility — measures how much a stock has actually moved over some past window. It is computed from daily price changes: take each day's return, measure how widely those returns are spread, and annualize the result so it sits on the same scale as implied volatility.

Options Band computes HV20 and HV60, realized volatility over the past 20 and 60 trading days, from daily closing prices. The short window reacts quickly to a change in a stock's behavior; the long window smooths it out.

Where implied volatility looks forward, HV looks strictly backward — it describes what happened, not what the option market expects next.

深入了解

The standard recipe uses close-to-close log returns:

• Compute each day's return: the natural log of today's close divided by yesterday's close.
• Take the standard deviation of those returns over the window (20 days for HV20).
• Multiply by √252, the square root of the number of trading days in a year.

A worked example with round numbers:

• Window: 20 trading days
• Standard deviation of daily returns: 1.5%
• Annualization factor: √252 ≈ 15.9

HV20 = 1.5% × 15.9 ≈ 24%. In plain terms: over the past month the stock has moved like a stock whose typical year spans a one-standard-deviation range of about ±24%.

Window choice matters more than it first appears. A single 8% earnings-day move inside a 20-day window lifts HV20 sharply — and then drops out of the calculation 20 trading days later even though nothing new happened. HV60 dilutes single days but is slower to register a genuine change in regime. Comparing HV20 with HV60 on the volatility dashboard shows whether recent movement is running above or below the stock's own recent norm.

Setting HV beside IV30 is the classic descriptive comparison: it shows the premium or discount the option market places on future movement relative to delivered movement. The two frequently diverge, especially ahead of scheduled events, when IV can climb while realized volatility stays quiet.

选读：详细说明 随堂练习不涉及此内容

The close-to-close estimator is

HV = √252 × stdev( ln(P_t ÷ P_t−1) ), taken over the chosen window

Log returns are used because they add across days. Some implementations assume a zero mean rather than subtracting the sample mean, which changes little at daily frequency. The √252 convention annualizes by trading days; annualizing by calendar days gives a different but internally consistent scale, so cross-source comparisons require knowing the convention in use.

Limitations: the close-to-close estimator captures overnight gaps but ignores intraday range entirely — a stock that swings 4% intraday and closes flat registers a quiet day. Range-based estimators (Parkinson, Garman-Klass, Yang-Zhang) use highs and lows to extract more information per day at the cost of extra assumptions. Estimator noise is also real: with only 20 observations, sampling error on a volatility estimate can run to several points.

A common misconception is treating HV as the "true" volatility against which IV is merely an opinion. Both are estimates of a latent quantity: HV estimates yesterday's, IV prices tomorrow's, and neither is automatically the benchmark.