Yang-Zhang vs Close-to-Close Volatility: Formulas, Worked Example and a 10-Year Study

This is a reference for the five daily-bar estimators: what each one measures, the formulas with their sources, a worked NVDA calculation you can check line by line, and two original studies. The first is a simulation where the true volatility is known. The second covers 20 US stocks and ETFs from 2017 to 2026 and asks how far the estimators disagree, which one tracks intraday data best, which forecasts best, and how often the choice flips an IV-RV signal. Every number on the page is in the free download pack.

Which realized volatility estimator should you use?

Use Yang-Zhang for US stocks and ETFs when you have clean daily open, high, low and close prices. Use close-to-close when you only have closes, when the highs and lows are unreliable, or when you need the number everyone else computes. The table matches the choice to the situation; the evidence for each row is further down the page.

Table 1. Choosing an estimator.

The widely shared table of "1, 5.2, 7.4, 8, 14" comes from a 2012 bank research note [7], not from the original papers. Parkinson's estimator is about 4.9 times as efficient as one squared return, Rogers-Satchell about 6.0 with zero drift, and Yang-Zhang's 14 is its maximum for a 2-day window [5][6].

What quantity are we estimating?

All five estimators target the same thing: the variance of the daily log return, measured from one close to the next. That day has two parts. The overnight part runs from yesterday's close to today's open; the session part runs from the open to the close.

The estimators differ in which pieces of the bar they read. Close-to-close sees only \(r_i\). Parkinson sees only the session's high and low. Garman-Klass and Rogers-Satchell see the whole session but not the gap. Yang-Zhang sees both parts. Each estimator returns a daily variance; this page annualizes it as \(100\sqrt{252 \times \text{variance}}\) to get volatility in percent.

Variance or volatility? The sample variance is unbiased, but its square root is not: a 20-session close-to-close volatility reads about 1.2% below the true value on average, and about 2.6% at 10 sessions (Study 1). Average variances, not volatilities, when you combine windows.

The shared assumptions. The theory behind every range estimator assumes the log price is a random walk with constant volatility inside the window, observed continuously, without bid-ask noise. Real prices are observed at discrete times, so the recorded high is below the true high and the recorded low above the true low, which pulls range estimators down [2][3][4]. Yang-Zhang also assumes the overnight and session returns are independent of each other.

The five estimators: formulas, assumptions and limits

Notation for a window of \(n\) bars: \(o_i\), \(c_i\) and \(r_i\) as above, \(u_i = \ln(H_i/O_i)\), \(d_i = \ln(L_i/O_i)\). A bar over a symbol is its mean over the window. These are the definitions the FlashAlpha API uses.

Close-to-close

The sample variance of daily log returns. Removing the mean makes it unaffected by drift, and because \(r_i = o_i + c_i\) it includes the overnight move. Its weakness is noise: one number per day. A common variant skips the mean and divides by \(n\) (zero-mean, as in many risk systems). The two differ most when the window trends, because the zero-mean version counts the trend as variance.

Parkinson (1980)

The constant \(1/(4\ln 2)\) converts the expected squared range of a driftless random walk into its variance. Parkinson ignores the open and close, so it misses the overnight gap and is biased by drift: a steady trend widens the range without adding variance. Efficiency is about 4.9 [4].

Garman-Klass (1980)

This is the form most software implements. It contains no previous close, so it does not see the overnight gap. Garman and Klass also gave a version that adds the gap with weight \(a = 0.12\), where \(f\) is the fraction of the day the market is closed: \(\sigma^2 = a\,(\ln O_i - \ln C_{i-1})^2/f + (1-a)\,\sigma^2_{\text{GK}}/(1-f)\), efficiency about 8.4 [2]. The session-only form is about 7.4 times as efficient as the squared open-to-close return [4], and is biased by drift.

Rogers-Satchell (1991)

Unbiased for any drift, which is what it was designed for. It still misses the overnight gap. Efficiency is about 6.0 with zero drift and above 2 for any drift [4]; the "8" in many tables is not supported by the theory. Rogers and Satchell also show that discrete observation biases the estimate down and give a correction [3].

Yang-Zhang (2000)

\(\sigma^2_o\) and \(\sigma^2_c\) are the sample variances of \(o_i\) and \(c_i\) (mean removed, divided by \(n-1\)); \(\sigma^2_{\text{RS}}\) is Rogers-Satchell. Yang and Zhang show the estimator is unbiased in the continuous limit, independent of drift and consistent with opening jumps, and that it has "the smallest variance among all estimators with similar properties" [5]. That is the class its optimality applies to. The 0.34 comes from \(\alpha - 1\) with \(\alpha = 1.34\), the value the authors suggest for small drift [5][8].

Under the paper's assumptions its efficiency relative to close-to-close depends on \(f\), the share of daily variance that happens overnight [5]:

With no overnight variance it is \(1/k\): 12.8 at \(n = 2\) and 7.2 at \(n = 20\). Its maximum, \(1 + 1/k\), is reached when a share \(k/(1+k)\) of the variance is overnight (about 12% at \(n = 20\)): 13.8 at \(n = 2\) and 8.2 at \(n = 20\). The "14 times" figure is that maximum for a 2-day window [6]. As the overnight share grows, the overnight term carries more of the variance and is estimated from \(n\) gaps, like close-to-close, so the advantage falls toward 1: at 40% overnight and 20 days the formula gives 4.8. Study 1 checks it.

Worked example: NVDA, 10 sessions with an earnings gap

NVDA reported earnings after the close on November 19, 2025. The next morning it opened 4.9% higher, then fell 8.1% during the session. In six of the 10 sessions from November 13 to November 26, the stock moved against its overnight gap during the session, including after the two largest gaps. Every input is in Table 2 and in the CSV; the close on November 12 seeds the first overnight return.

Table 2. NVDA daily bars and the per-bar terms. o = ln(O/C_prev), c = ln(C/O), r = o + c, u = ln(H/O), d = ln(L/O), RS term = u(u − c) + d(d − c). Log returns in percent; the CSV download has full precision.

1. Means. \(\bar o\) = -0.2245%, \(\bar c\) = -0.4998%, \(\bar r\) = -0.7243%.
2. Sample variances (divide by \(n - 1 = 9\)): \(s_o^2\) = 0.00072303, \(s_c^2\) = 0.00104499, \(s_r^2\) = 0.00060893. The last one is the close-to-close daily variance.
3. Range terms. Mean RS term = 0.00075720; \(\sum \ln(H/L)^2\) = 0.02322874; mean Garman-Klass term = 0.00078848.
4. Yang-Zhang weight for \(n = 10\): \(k = 0.34 / (1.34 + 11/9)\) = 0.132697. Then combine the three terms and annualize:

Yang-Zhang reads 22.7 points above close-to-close, and the 5-minute benchmark for the same sessions (59.3%) sits close to Yang-Zhang. Close-to-close sees only the net move on each reversal day: on November 20 it records −3.2% where the stock travelled 4.9% up and 8.1% down. The three session-only estimators see the session ranges but not the gaps. If your code reproduces Table 3 to two decimals from Table 2's bars, it matches this page and the FlashAlpha API's definitions.

Try it with your own bars

Four cases that show where each estimator breaks

Each card is one constructed week: five sessions after a prior close of 100, drawn as candles (dashed blue = overnight gap), with the annualized volatility each estimator reports. The spreadsheet recomputes them with live formulas.

Why can Yang-Zhang be lower than close-to-close?

Both estimators include the overnight move, so readers often expect Yang-Zhang to agree with close-to-close on average and to differ only by noise. On the same bars, the close-to-close variance splits exactly into an overnight part, a session part and their covariance:

So the gap between them has two sources:

• The range part, \((1-k)(s^2_{\text{RS}} - s^2_c)\). When sessions trade wide ranges but close near the open, Rogers-Satchell exceeds the open-to-close variance and Yang-Zhang moves up. Narrow ranges with directional closes move it down.
• The covariance part, \(-2\,\text{Cov}(o,c)\). Gaps that reverse during the session (negative covariance) push Yang-Zhang above close-to-close, because close-to-close nets the two legs. Gaps that continue push it below.

In the NVDA window, in annualized variance (volatility points squared): close-to-close 1,534.5, range part −629.0, covariance part +2,920.9, which sum to Yang-Zhang's 3,826.4 (= 61.86²). The whole gap comes from reversals; the range part pulls the other way. The practical point: Yang-Zhang minus close-to-close is not a measure of overnight risk. It measures how gaps and sessions co-move and how wide the sessions trade.

Across 20 symbols from 2017 to 2026, Yang-Zhang was below close-to-close in 33% to 53% of 20-session windows (average 45%). The median overnight-session correlation is close to zero for every symbol, so both parts are small on a typical day and large in specific windows.

Study 1: simulation with known volatility

The papers' efficiency figures assume ideal conditions. To see what each estimator delivers when those conditions fail, we simulated prices with a known volatility and measured each estimator's error.

Table 5. Efficiency relative to close-to-close by window length, ideal conditions (no gaps, no drift, 4,680 price steps a day). Efficiency = variance of the close-to-close variance estimate divided by the variance of the other estimate. Yang-Zhang theory with no overnight variance is 1/k; 1 + 1/k is its maximum, reached when a share k/(1 + k) of the variance is overnight.

With no gaps, the simulated Yang-Zhang efficiency lands 4% to 8% above \(1/k\): prices recorded at discrete times give slightly smaller ranges, which lowers the variance of the range terms along with their level (the accuracy measure in Figure 7 also counts that bias). With overnight gaps the formula tracks the simulation within 4% for overnight shares from 20% to 70% at 20 days; at 40% the 240,000-day scenario measured 4.75 against 4.76 predicted. Efficiency falls as the window grows because close-to-close spends one of its \(n\) observations on estimating the mean, which costs less as \(n\) grows.

Study 2: 20 US stocks and ETFs, 2017 to 2026

How far apart are the estimates?

Table 6. Distance from close-to-close by lookback, 20 symbols, every trading day from Jan 3, 2017 to Oct 30, 2026. Median and 90th percentile of the absolute difference in volatility points, and the median ratio to close-to-close.

Yang-Zhang and close-to-close differ by a median 1.97 points over 20 sessions, and by 6.6 points or more in one window in ten. The gap shrinks with the window (2.81 at 10 sessions, 1.24 at 60) because both converge to the same quantity. The session-only estimators do not converge: Parkinson stays about 4.50 points below at 60 sessions, because missing the overnight move is a bias, not noise.

Which estimate tracks intraday data best?

Yang-Zhang was closer to the benchmark than close-to-close on all 11 symbols, with a median bias of 1.3% or less. The session-only estimators read 17% to 55% low, worst for TLT, GLD and EEM, whose underlying markets trade while US equity exchanges are closed. Treat this as agreement with a second estimate, not distance from the truth: the benchmark shares the overnight returns with close-to-close and Yang-Zhang, and 5-minute sampling has its own noise.

Measuring the past vs forecasting the future

The sections above measure how well each estimator describes the window it covers. A different question is how well today's estimate predicts the next month. The two can disagree: an estimator can be precise about the past and still be a poor forecast if volatility changes.

We used each estimate as-is, with no fitted parameters, as the forecast of the mean daily variance over the next 21 sessions. That makes the test out of sample by construction. The target was measured two ways: the next 21 squared close-to-close returns (20 symbols) and the 5-minute benchmark (11 symbols). Losses use QLIKE, which ranks forecasts correctly even when the target is a noisy proxy [9]. Because the session-only estimators are biased low, we also report a calibrated version that rescales each estimate using only earlier, fully observed periods.

Table 8. Forecasting the next 21 sessions from today's estimate, out of sample. QLIKE loss relative to close-to-close (median across symbols; below 1 = better), and the number of symbols where the difference is significant at 5% (Diebold-Mariano, Newey-West, 25 lags), before and after a Holm correction across symbols. "Calibrated" rescales each estimate by the ratio of realized to estimated variance over all earlier, fully observed periods (at least 252). All versions are scored on the same dates per symbol (1,255 to 2,178 forecasts).

↑ = significantly better than close-to-close, ↓ = significantly worse, count of symbols. Holm: the same count after controlling the family-wise error rate at 5% across the symbols in that cell.

• Short windows: Yang-Zhang's 10-session estimate cut QLIKE loss to 0.68 of close-to-close's and was significantly better on all 20 symbols, all 20 after a Holm correction (and 11 of 11 against the 5-minute benchmark). The calibrated range estimators did about as well (0.64 for Parkinson).
• 20 sessions: Yang-Zhang 0.84, ahead on 19 of 20 symbols, significant on 13 before and 5 after the correction (6 and 3 of 11 against the benchmark). Treat this as a tendency, not a firm result. Uncalibrated Parkinson was worse than close-to-close (1.52) because of its level bias, and competitive once calibrated (0.88).
• 60 sessions: the estimator barely matters (0.95 for Yang-Zhang). With long windows, noise averages out and the level of volatility changes faster than any trailing estimate can follow.

A trailing estimate is a baseline, not a model. Our earlier study of volatility forecasts for option sellers tested EWMA, HAR, GARCH and HEAVY on the same symbols; at a one-month horizon none of them beat 30-day implied vol.

What this means for IV-RV comparisons and earnings

Two different quantities both get called the volatility risk premium:

• Trailing IV minus RV: implied vol today minus realized vol over the past window. Known today, and what most dashboards show, including FlashAlpha's vrp_20d.
• The forward premium: implied vol (or variance) today minus the volatility realized over the option's life. Known only afterwards. Academic measures define it in variance terms and match the horizons, for example the variance swap rate against the realized variance over the contract [10]; others pair implied variance with the past month's realized variance [11].

Table 9. 30-day ATM implied vol minus trailing 20-session realized vol, by estimator. 11 symbols, 2017 to 2026. Spread statistics use all 25,874 symbol-days with today's inputs; the forward premium (implied vol minus the 5-minute benchmark over the next 21 sessions, about 30 calendar days) and the correlation use the 23,326 days whose next 21 sessions are known.

With close-to-close, the 20-session spread was positive on 62% of days (median 1.3 points); with Yang-Zhang on 63% (median 1.1); with Parkinson on 93% (median 5.5), because Parkinson misses the overnight move. A rule such as "sell when IV exceeds RV by 4 points" gives a different answer than with close-to-close on 13.8% of days with Yang-Zhang and 43.2% with Parkinson. None of the trailing spreads tracked the forward premium closely (correlations 0.02 to 0.08); the forward premium itself had a median of 1.4 points and was positive on 65% of days. Read a trailing spread as a description of the recent past, and state which estimator it uses.

Earnings. Trailing windows and implied vol treat a scheduled event differently. Before a report, 30-day implied vol prices the coming move and trailing realized vol does not, so the spread looks wide. After the report, the trailing window contains the move and implied vol no longer prices it. NVDA on November 26, 2025: 30-day implied vol was 39.9% (down from 52.6% before the report). Against the 10-session window above, IV minus RV was +0.7 points with close-to-close, -6.1 with Parkinson and -22.0 with Yang-Zhang; over 20 sessions, -2.2 and -14.7. Three estimators, three conclusions, and all of them mostly measure an event that has passed. To judge the event itself, compare the move implied for the next report with the stock's past earnings moves, which is what FlashAlpha's /v1/earnings/vrp/{symbol} returns (Alpha).

Data conventions and failure cases

Two correct implementations can disagree by several points because of data conventions, not formulas. State these when you publish a number, and check them when you reconcile with another source.

Table 10. Calculation specification used on this page and in the downloads.

Failure cases to test for: a high or low far outside its neighbours (bad print); an open equal to the previous close every day (a feed that fills missing opens, which zeroes the overnight term); a day with the open, high, low and close all equal (no trades); a split day without adjustment; and windows that mix trade-based and quote-based bars. Each one changes the range estimators far more than close-to-close.

Python reference implementation and downloads

The reference implementation computes all five estimators from arrays and keeps data retrieval separate. It reproduces Table 3 exactly and, run on FlashAlpha's own bars, matched every value of the live /v1/volatility/realized response for SPY and NVDA on November 10, 2026 (all 15 values, to 0.01).

import numpy as np

def components(o, h, l, c, prev_c):
    o, h, l, c, prev_c = (np.log(np.asarray(x, float)) for x in (o, h, l, c, prev_c))
    oc, u, d = c - o, h - o, l - o
    return {"o": o - prev_c, "c": oc, "r": (o - prev_c) + oc,
            "hl2": (h - l) ** 2, "gk": 0.5 * (h - l) ** 2 - (2 * np.log(2) - 1) * oc ** 2,
            "rs": u * (u - oc) + d * (d - oc)}

def window_variances(comp):
    n = len(comp["o"])
    k = 0.34 / (1.34 + (n + 1) / (n - 1))
    rs = comp["rs"].mean()
    return {"close_to_close": comp["r"].var(ddof=1),
            "parkinson": comp["hl2"].sum() / (4 * n * np.log(2)),
            "garman_klass": comp["gk"].mean(),
            "rogers_satchell": rs,
            "yang_zhang": comp["o"].var(ddof=1) + k * comp["c"].var(ddof=1) + (1 - k) * rs}

annualize = lambda var: 100 * np.sqrt(252 * var)

# NVDA, Table 2 (prev_c is the previous row's close; the first is Nov 12's 193.80)
# expected: close_to_close 39.17, parkinson 45.95, garman_klass 44.58,
#           rogers_satchell 43.68, yang_zhang 61.86

To run it on any symbol with public data, pin the download settings: in yfinance 1.x, yf.download returns multi-level columns and adjusts prices by default. yf.Ticker("SPY").history(period="1y", auto_adjust=False) returns flat Open, High, Low, Close columns, split-adjusted but not dividend-adjusted, which is the convention used here. Tested with yfinance 1.2.0, pandas 2.3.3 and NumPy 2.3.5.

The files are free with a FlashAlpha account. Sign in or create one, and the download starts. Everything on this page stays open to read.

The research pack (v1.1) holds everything needed to rerun both studies: the code, the FlashAlpha benchmark and implied vol inputs for the 11 benchmark symbols, the published results, and manifest.json with the SHA-256 hash, row count and date range of every input file. The Yahoo bars are downloaded by fetch.py; compare them with the manifest, because Yahoo can revise history. study.py --public-only reruns the agreement, condition, decomposition and squared-return forecast results from the Yahoo bars alone.

Get all five estimators from the FlashAlpha API

/v1/volatility/realized/{symbol} returns close-to-close, Parkinson, Garman-Klass, Rogers-Satchell and Yang-Zhang over 10, 20 and 30 sessions in one call, using the definitions on this page. It needs the Alpha plan. The API computes from split-adjusted daily bars built from FlashAlpha's quote archive, so its values can differ from a calculation on exchange trade bars such as the Yahoo bars in this study.

import httpx

r = httpx.get("https://lab.flashalpha.com/v1/volatility/realized/NVDA",
              headers={"X-Api-Key": "YOUR_API_KEY"}, timeout=30)
r.raise_for_status()
est = r.json()["estimators"]
for name in ("close_to_close", "parkinson", "garman_klass", "rogers_satchell", "yang_zhang"):
    print(f"{name:16s} rv10 {est[name]['rv10']:6.2f}  rv20 {est[name]['rv20']:6.2f}  rv30 {est[name]['rv30']:6.2f}")

curl -H "X-Api-Key: YOUR_API_KEY" \
  "https://lab.flashalpha.com/v1/volatility/realized/NVDA"

Two related endpoints: /v1/volatility/forecast/{symbol} (Alpha) returns EWMA, HAR, GARCH and realized-measure model forecasts for 1, 5 and 21 sessions next to 30-day implied vol, and /v1/volatility/{symbol} (Growth) returns close-to-close realized vol over 5 to 60 days with ATM implied vol and IV-RV spreads. To compare estimators on one symbol, use the CC and YZ values from the same /realized response so the bars are identical.

Limitations

• The market study covers 20 large, liquid US symbols; smaller stocks have wider spreads and more bad prints, which favours close-to-close.
• The bars (exchange trades) and the benchmark (quote midpoints) come from different sources, so part of the measured distance is source difference.
• Rolling windows overlap; the forecast tests correct for this with Newey-West variances, the descriptive percentiles do not.
• QLIKE ranks forecasts correctly when the target is conditionally unbiased for the variance [9]. Squared returns meet that; the 5-minute benchmark does only approximately, so we report both targets.
• The testing family for the Holm correction (symbols within each target, window and estimator) was chosen after the first release, as a robustness check.
• Earnings dates come from Yahoo Finance and were not checked against company filings.
• The simulation uses constant volatility and normal returns; real returns have fat tails and volatility clustering.

Related reading

• How to calculate the volatility risk premium
• Realized vs implied volatility and the risk premium
• Do volatility forecasts help option sellers?
• SPY volatility cone: 8 years of data
• Realized volatility (concept)

Frequently asked questions

References

1. Parkinson, M. (1980). The extreme value method for estimating the variance of the rate of return. The Journal of Business, 53(1), 61-65. https://doi.org/10.1086/296071
2. Garman, M. B., & Klass, M. J. (1980). On the estimation of security price volatilities from historical data. The Journal of Business, 53(1), 67-78. https://doi.org/10.1086/296072
3. Rogers, L. C. G., & Satchell, S. E. (1991). Estimating variance from high, low and closing prices. The Annals of Applied Probability, 1(4), 504-512. https://doi.org/10.1214/aoap/1177005835
4. Molnár, P. (2012). Properties of range-based volatility estimators. International Review of Financial Analysis, 23, 20-29. https://doi.org/10.1016/j.irfa.2011.06.012
5. Yang, D., & Zhang, Q. (2000). Drift-independent volatility estimation based on high, low, open, and close prices. The Journal of Business, 73(3), 477-492. https://doi.org/10.1086/209650
6. Brandt, M. W., & Kinlay, J. (2005). Estimating historical volatility [Working paper]. https://doi.org/10.2139/ssrn.4384038
7. Bennett, C., & Gil, M. A. (2012). Volatility trading: Trading volatility, correlation, term structure and skew. Santander Investment Bolsa.
8. Vințe, C., & Ausloos, M. (2022). The cross-sectional intrinsic entropy: A comprehensive stock market volatility estimator. Entropy, 24(5), 623. https://doi.org/10.3390/e24050623
9. Patton, A. J. (2011). Volatility forecast comparison using imperfect volatility proxies. Journal of Econometrics, 160(1), 246-256. https://doi.org/10.1016/j.jeconom.2010.03.034
10. Carr, P., & Wu, L. (2009). Variance risk premiums. The Review of Financial Studies, 22(3), 1311-1341. https://doi.org/10.1093/rfs/hhn038
11. Bollerslev, T., Tauchen, G., & Zhou, H. (2009). Expected stock returns and variance risk premia. The Review of Financial Studies, 22(11), 4463-4492. https://doi.org/10.1093/rfs/hhp008
12. Shu, J., & Zhang, J. E. (2006). Testing range estimators of historical volatility. Journal of Futures Markets, 26(3), 297-313. https://doi.org/10.1002/fut.20197
13. Alizadeh, S., Brandt, M. W., & Diebold, F. X. (2002). Range-based estimation of stochastic volatility models. The Journal of Finance, 57(3), 1047-1091. https://doi.org/10.1111/1540-6261.00454

Further reading on range estimators in real markets: Shu and Zhang find the estimators close to integrated variance on S&P 500 data but sensitive to opening jumps and large drift [12]; Alizadeh, Brandt and Diebold show range-based proxies are efficient and robust to microstructure noise [13].

How to cite this page

@misc{flashalpha_yz_cc_2026,
  author       = {Dobrowolski, Tomasz},
  title        = {Yang-Zhang vs Close-to-Close Volatility: Formulas, Worked Example and a 10-Year Study},
  year         = {2026},
  version      = {1.1},
  publisher    = {FlashAlpha},
  url          = {https://flashalpha.com/articles/yang-zhang-vs-close-to-close-realized-volatility},
  note         = {Accessed: YYYY-MM-DD}
}
@misc{flashalpha_rv_study_2026,
  author       = {FlashAlpha},
  title        = {Realized Volatility Estimator Study},
  year         = {2026},
  version      = {1.1},
  howpublished = {Data set and code},
  url          = {https://flashalpha.com/downloads/realized-volatility-estimators/realized-volatility-study-v1.1.zip}
}

Changelog. Version 1.1 (2026-11-10): Yang-Zhang theory comparator corrected (\(1/k\) with no gaps; \(1 + 1/k\) is the maximum), Holm-adjusted forecast counts, raw and calibrated forecasts scored on identical dates, IV-RV signal statistics on all days with today's inputs, the benchmark specified in full, and its inputs added to the research pack with a manifest and a public-only mode. Version 1.0 (2026-11-10): rewritten as a reference with corrected efficiency figures (Yang-Zhang 1 + 1/k; Parkinson 4.9; Rogers-Satchell 6.0), the session-only Garman-Klass form identified as such, close-to-close correctly described as unaffected by drift, a hand-checkable NVDA example replacing an illustrative one, and two original studies. First published March 17, 2026.

Conclusion

Close-to-close and Yang-Zhang measure the same close-to-close variance; Yang-Zhang gets there with fewer days by reading the open, high and low, and it counts the overnight move that Parkinson, Garman-Klass and Rogers-Satchell miss. The efficiency gain at 20 days is 7.2 times with no overnight gaps and at most 8.2, not 14, and it shrinks when gaps dominate or the highs and lows are dirty. On real data the choice moves a 20-day reading by 1.97 points at the median and much more around gaps and earnings, enough to flip an IV-RV signal on 17.3% of days. Pick one estimator, state it, and check your numbers against the worked example. Or pull all five from the realized volatility endpoint on the Alpha plan.