Implied Volatility Suite: Formula and Data Limits
The IV Suite calculations examined here use chart prices. They do not read option premiums or solve an option-pricing model, so their outputs do not establish market-implied volatility, option richness or put/call skew. This guide explains the price proxies and provides a complete reference with explicit units and ranking rules.
Inspect the Pine ScriptMarket-implied volatility needs an option price
The Options Industry Council explains implied volatility as a value inferred from option prices through a pricing model. A calculation needs the relevant contract, strike, expiry, observed premium and applicable model inputs. Historical returns alone do not identify what traders are paying for that contract.
The displayed reference uses only the chart’s close and low. It has no option quote, contract selection, bid/ask spread, interest-rate input or pricing-model inversion. Changing a price lookback to match a contract’s days to expiry does not supply those missing observations.
Likewise, Cboe’s VIX methodology uses SPX option prices to construct a constant 30-day measure. The legacy default of 45 in this price-based code is not the VIX horizon. A VixFix-style price-range calculation is not a reproduction of that options index.
What the legacy model actually computes
The return input is ln(close[1] / close[2]), so it is delayed one chart bar. Let N be the return lookback, μ its mean and s its population standard deviation. The legacy model’s unhalved proxy simplifies to exp(Nμ) × sinh(s√N) / √(N/365), where sinh(z) = (exp(z) − exp(−z)) / 2. The current spot cancels out of the original upper/lower-width formula.
The formula transforms historical returns and hard-codes a factor involving 365. It is not an option-price inversion or the usual historical-volatility formula s√A. Its drift term exp(Nμ) means the average return affects the result as well as dispersion. The “days” parameter in the legacy function is used as a count of chart bars; an hourly chart does not magically supply daily returns.
The original main model also halves sigma whenever sigma > 1. This is not a cap at 100%: 0.999 stays 0.999, 1.001 becomes 0.5005, and 3 becomes 1.5. It introduces a downward discontinuity and can reverse the ordering of nearby observations. The reference exposes that behavior as an explicit legacy-reproduction toggle rather than presenting it as a justified volatility correction.
The legacy minutes and hours feed an expiry variable used in other helper calculations; they do not change the main model formula above. The reference omits those unused-for-this-output controls. For conventional return dispersion, inspect the separate Historical Volatility guide.
The price-range branch and its units
In the legacy range branch, the upside and downside helpers receive a deviation multiplier of zero. Their price adjustments disappear, so both reduce to 100 × (highest close over N bars − current low) / highest close. Averaging the identical results changes nothing.
For a hypothetical highest close of 100 and current low of 95, this proxy is 5. It describes a price-range distance of 5%, not an annualized volatility or an option IV of 5%. The reference displays it once on that scale. Multiplying this already-percentage result by 100 again would display 500 and create a unit error.
The reference requires positive, available close and low with low no greater than close, plus a complete range window. It does not interpret this range measure as put demand, buying pressure or a quoted premium. It can be calculated without an options market precisely because it uses no options information.
Range rank and percentile answer different questions
Range rank = 100 × (current − window minimum) / (window maximum − window minimum). A rank of 80 locates the value 80% of the distance from minimum to maximum; it does not say that 80% of observations were lower. Rank 50 is the midpoint of the extremes, not necessarily the median.
This reference defines its percentile explicitly: count values strictly below the current proxy in a window that includes the current bar, divide by the window length, and multiply by 100. Ties do not count as below. It uses a loop rather than claiming equivalence with every platform’s percentile convention.
Take five synthetic values [10, 10, 10, 20, 18], with 18 current. The range rank is (18 − 10)/(20 − 10) × 100 = 80. The strict-below percentile is 3/5 × 100 = 60. For [10, 18, 18, 20, 18], range rank remains 80 but the strict-below percentile is 20. The same min/max position can describe different distributions.
With this inclusive-window convention, even a unique new high has percentile 100 × (N−1)/N because it is not below itself. An all-equal window has strict-below percentile 0 and undefined range rank, which the code leaves blank. A denominator policy and a tie policy must be specified before comparing implementations.
Price asymmetry is not an options skew surface
Option skew compares implied volatilities across contracts, commonly strikes at the same expiry. Price-only upside/downside transformations do not measure those contracts. Their difference cannot tell you that calls or puts are expensive, even if a variable is named Skew_Index.
The legacy model-skew expression averages three repeated calls with identical arguments on each side; it is not three separately weighted option observations. Other range-skew helpers perturb price series by standard deviation. Those operations still supply no option prices. This reference therefore provides raw proxy, range rank and a stated percentile, without an option-skew output.
If actual contract IV is the intended input, use a documented quote source and record contract terms, quote time, price selection and model convention. Reconcile the IV first, then compute ranks over a consistent tenor and moneyness definition. Mixing changing contracts without a definition can make a historical rank difficult to interpret.
A reproducible use boundary
Use the proxy as a descriptive price-derived series and verify a closed-bar value. The log-return branch waits for N valid delayed returns; the range branch waits for N valid price bars. Rank and percentile require a further complete window of valid proxy values. The two methods have different meanings even when both raw displays use a percent sign.
The range branch and its rank can change as the current low develops. The lagged-return model excludes the current bar’s return. The source adds no alerts, bar-close gate or trades. A 365-bar daily equity window is not one calendar year of trading sessions; intraday windows depend on the actual session and bar count.
A high rank does not establish an overpriced option, a mean-reversion date or permission to increase short-option exposure. This page provides no tested premium-selling rule or strategy return. Real options evaluation needs contract quotes, costs, exercise/assignment behavior, settlement and position risk in addition to any volatility statistic.
Pine Script v6: implementation and limits
This is a complete price-proxy teaching reference with explicit controls, units, window validity and a strict-below percentile definition. It retains an optional legacy halving rule for inspection. It does not implement the legacy skew helpers or claim identical output to every generated suite configuration.
//@version=6
indicator("IV Suite: price-proxy audit reference", overlay=false, precision=4)
method = input.string("Legacy model proxy", "Price-derived method", options=["Legacy model proxy", "VixFix price range"])
modelLength = input.int(45, "Model return bars", minval=2, maxval=500)
rangeLength = input.int(252, "Price-range bars", minval=2, maxval=500)
rankLength = input.int(365, "Rank window including current bar", minval=2, maxval=500)
outputMode = input.string("Range rank", "Output", options=["Raw proxy", "Range rank", "Strict-below percentile"])
legacyHalving = input.bool(true, "Reproduce legacy sigma > 1 halving")
// These are lagged chart-bar returns, not option-price observations.
logReturn = close[1] > 0 and close[2] > 0 ? math.log(close[1] / close[2]) : na
modelReady = math.sum(na(logReturn) ? 0.0 : 1.0, modelLength) == modelLength
meanReturn = ta.sma(logReturn, modelLength)
returnSd = ta.stdev(logReturn, modelLength, true)
z = returnSd * math.sqrt(modelLength)
sigma = modelReady ? math.exp(modelLength * meanReturn) * (math.exp(z) - math.exp(-z)) / (2 * math.sqrt(modelLength / 365.0)) : na
modelProxy = legacyHalving and sigma > 1 ? sigma / 2 : sigma
validPrice = not na(close) and not na(low) and close > 0 and low > 0 and low <= close
rangeReady = math.sum(validPrice ? 1.0 : 0.0, rangeLength) == rangeLength
highestClose = ta.highest(close, rangeLength)
rangeProxy = rangeReady and highestClose > 0 ? 100.0 * (highestClose - low) / highestClose : na
// Both raw outputs are displayed once on a percent scale; neither is option IV.
proxy = method == "Legacy model proxy" ? 100.0 * modelProxy : rangeProxy
rankReady = math.sum(na(proxy) ? 0.0 : 1.0, rankLength) == rankLength
windowLow = ta.lowest(proxy, rankLength)
windowHigh = ta.highest(proxy, rankLength)
rangeRank = rankReady and windowHigh > windowLow ? 100.0 * (proxy - windowLow) / (windowHigh - windowLow) : na
float strictPercentile = na
if rankReady
int below = 0
for i = 0 to rankLength - 1
below += proxy[i] < proxy ? 1 : 0
strictPercentile := 100.0 * below / rankLength
selected = outputMode == "Raw proxy" ? proxy : outputMode == "Range rank" ? rangeRank : strictPercentile
plot(selected, "Selected price-proxy statistic", color=color.blue)
plot(outputMode == "Raw proxy" ? na : 50.0, "Rank/percentile midpoint", color=color.gray)
Specify a checkable adaptation in Pineify
State whether you need a price proxy or actual contract IV. For a proxy, specify the exact formula, units, window, tie policy and confirmation timing. For option IV, identify a real quote source and pricing inputs before requesting code. Review the generated source and reconcile known values; syntax success cannot establish that missing market data exists.
Open Pine Script AI Coding AgentEducational indicator analysis. No measured trading performance is established here. Syntax validation does not prove formula equivalence, execution assumptions or profitability.