Greeks

How it works

An option's price depends on several things at once: where the underlying is, the strike, how long is left, how volatile the underlying is expected to be, the interest rate, and any dividends expected before expiry. The Options Industry Council lists exactly that set — stock price, strike price, time to expiration, implied volatility, interest rate, anticipated ordinary dividends — as the inputs a pricing model takes.

A greek is the answer to "how much does the model's value move if I change one of those and nothing else". The OIC's own definitions are that plain: delta is "a measure of the relationship between an option premium and the underlying stock price", gamma "the sensitivity of Delta to a one-unit change in the underlying", theta "the sensitivity of an option's premium to change in time", vega "the sensitivity of option value to changes in implied volatility", rho "the sensitivity of option value to change in interest rate".

The sentence to take away from the same source is that the greeks are "a collection of statistical values that help the investor better understand the potential impact changes in pricing model inputs might have on an option's value", and are "not a guarantee of exact option premium changes, but rather a theoretical guidepost". They describe a model. The market is under no obligation to agree with it.

Why they differ between two vendors

Nothing in a chain says which model produced its greeks, and the choice is genuinely open. The SEC's own guidance on valuing share-based payments — an option valuation that gets audited — says that it "does not specify a preference for a particular valuation technique or model", discusses closed-form Black-Scholes-Merton and lattice approaches alongside each other, and describes a "zone of reasonable conduct" in which different issuers reach different conclusions. That is a different context from a listed options feed, and it is the clearest official statement that an option value is a function of a chosen method rather than a reading.

Five inputs then vary underneath the model, and every one of them moves the output:

The volatility input. Usually an implied figure, which is itself a model inversion of an observed price, and vendors differ on which observed price and on whether the surface is smoothed before the greeks are taken off it. See implied volatility — this is the largest single source of disagreement.

The interest rate. A published methodology has to say where the rate comes from, and the good ones do: Cboe's volatility index mathematics, version 5.0 revised 26 February 2026, derives its risk-free rate from US Treasury constant maturity yields with a bounded cubic spline, converts bond equivalent yields to annualised yields and then to continuously compounded rates. A vendor that publishes nothing about its rate has still made all of those decisions.

The dividend assumption. Expected dividends before expiry, which for a single name is a forecast, not a fact.

Early exercise. US single-name equity options are American. A model that prices them as European is cheaper to run and wrong in a direction that grows with the dividend and the moneyness.

Which instant. A delta computed from an underlying price and an option quote sampled a second apart is a different number from one where both came from the same timestamp, and whether the option input was a last trade, a bid, an ask or a mid changes it again. The NBBO entry covers why "the quote" is not one number either.

Why it matters here

Three consequences for reading cards in this catalogue.

First, greeks are priced as a separate product because they are work, not data. Vendors here charge for them as an add-on or a tier — the pattern is visible across options data, and ORATS sells the surface itself as the product rather than the quotes. What you are buying is somebody's modelling and their commitment to maintaining it.

The same fact runs in reverse: a free chain that includes a greek is handing over somebody's undocumented model output at no charge, which is the part to treat carefully rather than as a bargain. How to get an options chain walks the free and cheap sources and says which of them carry greeks at all.

Second, do not mix sources in one row. A table with delta from one provider and vega from another asserts a consistency that was never computed. Same for stitching a history together across a vendor change: the discontinuity will look like a change in the market.

Third, if the numbers have to be defensible, compute them. QuantLib prices the instruments and builds the curves and supplies no data at all, which is exactly the division of labour this page argues for — buy the quotes, own the model, and write down the rate and dividend assumptions next to the output. A greek with its inputs recorded is a number somebody can check. A greek off a feed is a number somebody chose.