Implied volatility

How it works

Every other input to an option pricing model is observable: the underlying price, the strike, the days to expiry, a rate, a dividend estimate. Volatility is not. So the calculation is usually run the other way round — take the option's market price as given, and solve for the volatility number that makes the model return it. That number is the implied volatility, and the arrow of causation is the whole point: the price came first, the volatility is derived from it.

Two things follow immediately.

It is a model inversion, so it is model-dependent. Change the model and the same quote implies a different figure. The SEC's guidance on valuing share-based payments, which has to survive an audit, says plainly that it "does not specify a preference for a particular valuation technique or model", notes that "option-pricing models require an estimate of expected volatility as an assumption because an option's value is dependent on potential share returns over the option's term", and allows a company with actively traded options to place "greater (or even exclusive) reliance on implied volatility" only after weighing trading volume, strike similarity and comparable term. An official document declining to name one method is the clearest statement available that there is no single right answer to invert.

It is solved from one particular price, and nobody agrees which. Last trade, bid, ask, or the midpoint of the two — four defensible choices, four different numbers, and on an illiquid series the gap between them is not small. Cboe's volatility index mathematics, version 5.0 revised 26 February 2026, commits to the mid and says so: call and put prices "reflect the midpoint of each candidate constituent option series' bid / ask quotes", with a defined mid of bid plus ask over two, and series whose quotes are null or crossed are excluded outright. Making the convention explicit is what makes a published figure checkable.

That same document is worth reading for a second reason. The VIX family does not invert a Black-Scholes price at all — the methodology "is based on theoretical work in pricing variance swaps to isolate exposure to volatility of an asset", weighting constituent options inversely to the square of their strike. So "implied volatility" already names at least two different constructions: a per-contract model inversion, and an index built from a portfolio of options without a per-contract model. A number labelled IV on a chain is the first. A number labelled IV on an index is often the second.

Where vendors diverge after that

Smoothing and fitting. Raw per-contract implied volatilities are noisy, because the quotes they came from are noisy. Most serious providers fit a surface across strikes and expiries and publish the fitted value, which is a modelling decision applied on top of a modelling decision.

Quote filtering. Which series are dropped for being crossed, zero-bid, stale or off the pricing grid. Cboe's published algorithm excludes options with a bid or ask price equal to zero and applies a time-windowed quote filter; a vendor with no published rule has still made one.

The rate and dividend inputs, which feed the inversion exactly as they feed everything else. The greeks entry works through that set, and this page is its input rather than its sibling: vega is the sensitivity to this number, and the greeks are usually computed at the volatility solved here.

Snapshot timing. An implied volatility from an option quote and an underlying price taken a second apart is measuring the gap between the two clocks as much as anything else.

Why it matters here

For the cards in this catalogue the practical consequences are narrow and worth stating flatly.

An IV series from two providers cannot be stitched together. The discontinuity at the join is their methodologies changing, not the market, and it will look exactly like a real event. Same for an IV rank or percentile computed off a spliced history.

A smoothed surface is a different purchase from a chain. ORATS sells the surface as the product, going back years, which is what makes a consistent cross-sectional comparison possible at all; a plain chain from a general-purpose API gives you quotes and leaves the fitting to you. Cboe DataShop sells exchange files with implied volatility attached as a more expensive variant of the same day's summary, which prices the distinction honestly. Everything in the catalogue that touches the asset class is on options data, and how to get an options chain covers what the free tiers hand over.

And if the figure has to be reproducible, own the inversion. QuantLib supplies the models and no data; the NBBO entry covers which quote you should be inverting, and recording that choice is most of the difference between a number and a number somebody can check.