Two data sources, two time directions
OIC distinguishes measured historical variation from volatility inferred from current option prices. Start with the data definition before choosing an indicator. A single contract, an at-the-money series, and an index that combines many options can all be called IV while representing different observations.
| Record | Historical volatility | Implied volatility |
|---|
| Input | Underlying prices and a return estimator. | Option premium, underlying price, strike, time to expiry, and pricing-model assumptions. |
| Time period | A completed lookback, such as the last 20 daily returns. | The remaining life of a contract, or a specified constant maturity. |
| Choices that change the result | Sampling interval, session, adjustments, window, standard-deviation convention, and annualization. | Strike, expiry, call or put, bid or ask, timestamp, rates, dividends, and model. |
| Question answered | How dispersed were returns in this sample? | What volatility is consistent with this option price under the model? |
Recalculate HV before comparing the percentages
This constructed example uses 21 positive daily closes, starting at 100, with 20 log returns alternating +0.01 and −0.01. Each next close equals the previous close multiplied by exp(return), so the closes alternate approximately 101.0050167 and 100. Use the exact log returns for calculation, not rounded prices. Their mean is zero and their squared deviations sum to 0.002. At the final close of 100, assume a same-underlying call with strike 100, 30 calendar days remaining, and model-implied volatility of 24% from a contemporaneous quote. No market data is used.
- The sample denominator is N − 1. A population denominator of N would produce 15.874508% annualized HV from the same returns. Check the selected indicator implementation before expecting an exact match.
- Twenty returns require 21 closes. With fewer than two valid returns, this sample estimator is undefined. Zero or negative prices make this log-return definition invalid; missing prices must not silently become zero.
- Replacing 252 with 365, while keeping the same daily returns, produces 19.601289%. This is a convention sensitivity check, not a correction for weekends. Select a sampling calendar appropriate to the asset and document it.
| Step | Declared calculation | Result |
|---|
| Return definition | r = ln(current close / previous close) | 20 daily observations |
| Sample daily variance | 0.002 / (20 − 1) | 0.0001052632 |
| Sample daily standard deviation | sqrt(0.002 / 19) | 1.025978% |
| Annualized HV | 100 × sqrt(0.002 / 19) × sqrt(252) | 16.286901% |
| Hypothetical annualized IV | Assume a 30-calendar-day option quote of 24% | 24.000000% |
| IV minus HV | 24 − 16.286901 | +7.713099 percentage points |
Annualization does not align the observation windows
The 16.29% HV above summarizes the past 20 trading sessions. The assumed 24% IV concerns the next 30 calendar days. They form a historical baseline versus a forward quote, not two measurements of one period. An earnings release inside the option term but outside the historical window is one reason the comparison can change.
- Choose the research horizon first. For a roughly one-month comparison, record the actual past session dates and the exact future expiry. A 60-session HV may be a useful second baseline, but label it separately rather than replacing the shorter estimate after seeing the result.
- Under square-root-of-time scaling, 24% annualized IV corresponds to 24% × sqrt(30/365) = 6.880586% over 30 calendar days. Assuming 21 future trading sessions, the example HV gives 16.286901% × sqrt(21/252) = 4.701623%. These are illustrative scaled standard deviations, not guaranteed price ranges or exact probabilities.
- Time scaling assumes variance grows proportionally with time. Jumps, changing volatility, and dependence between returns can make that approximation poor. Annualizing five-minute returns requires a declared intraday calendar and overnight treatment; multiplying a daily factor by an arbitrary bar count does not recover missing overnight risk.
- Constant-maturity IV and a listed option expiry are different series. Cboe VIX combines SPX options into a 30-day measure; it is not the IV of an individual stock. Comparing stock HV with VIX adds an underlying mismatch.
Collect comparable observations in TradingView
For HV, record the exact exchange symbol, price adjustment, chart session, return interval, indicator length, and formula. TradingView provides a Historical Volatility indicator, but this page specifies its own estimator for the arithmetic example. Do not assume every community script or screener field labelled volatility uses the same calculation.
- For IV, open Products → Options and select the underlying. TradingView documents expiry and strike filters and separate Bid IV and Ask IV columns. Record the contract, expiry, strike, option side, underlying price, and quote timestamp alongside the chosen IV value.
- Keep the quote convention consistent. If hypothetical bid IV is 22% and ask IV is 26%, the same 16.286901% HV gives gaps of 5.713099 and 9.713099 points. An apparent difference smaller than that quote uncertainty needs scrutiny. The midpoint of bid and ask IV is not necessarily the IV computed from the midpoint option premium.
- Compare observations available at the same decision time. A live option quote versus a previous-day HV is a deliberate timing choice that needs a label. Missing or stale quotes are unavailable data, not zero volatility.
- A visible options-chain field does not establish that Pine can request its historical series. Confirm a supported symbol or data path before designing a historical IV filter. A manually entered current IV can illustrate a snapshot; it cannot reconstruct a historical backtest.
What a positive IV-HV gap does and does not establish
The example establishes only that the chosen annualized IV exceeds the selected historical estimate by 7.71 points. It does not establish that the option is mispriced. Future realized volatility is still unknown, and a volatility comparison alone leaves out the option payoff, execution costs, and hedge behavior.
- IV minus trailing HV is not a clean measurement of the variance risk premium. It mixes a forward quote with past realized behavior; variance-based comparisons also square volatility and require matched definitions.
- To evaluate a forecasting rule, save the IV observation and its data availability time, then measure realized volatility over the subsequent specified horizon. Define the estimator before collecting results and retain losing or inaccurate cases. This evaluates the rule without claiming that trailing HV was the future outcome.
| Hypothetical observation | Permitted interpretation | Unsupported conclusion |
|---|
| IV 24%; recent HV 16.286901% | The option quote implies more volatility than this past-window estimate. | Selling the option will earn 7.71%. |
| IV 24%; a separately measured longer-window HV of 25% | The sign changes to −1 point when the historical baseline changes. | Options must be cheap or a price rise is likely. |
| High IV before a scheduled event | The option period includes event uncertainty. | The size or direction of the event move is known. |
Write the selected comparison as an explicit rule
After choosing the data and horizon, use the Pine Script AI Coding Agent to draft an HV display or a filter from those explicit rules. A useful specification names the return interval, lookback, sample or population denominator, annualization factor, and missing-data behavior. Include the numeric example above as a calculation check.
- If IV is a manual input, label it as a dated snapshot and prevent it from being presented as historical IV. If it is a series, specify its source, maturity definition, and availability delay.
- Request syntax validation, inspect the generated source, and compare its readings with independently calculated values. Syntax checks do not validate quote quality, financial assumptions, or profitability. Pineify does not turn missing IV history into observed data.
