# Greeks

Also written option greeks.

*https://stockmarketstack.com/glossary/greeks · next to Stock Market Data APIs*

**Definition:** Sensitivities of an option's theoretical value to one input at a time: delta to the underlying price, gamma to delta itself, theta to time, vega to volatility, rho to the interest rate. They are outputs of a pricing model rather than observations of the market, so they carry every assumption that model makes, and two vendors publishing greeks for the same contract will disagree without either being wrong.

## 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](https://stockmarketstack.com/glossary/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](https://stockmarketstack.com/glossary/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](https://stockmarketstack.com/collections/options-data), and [ORATS](https://stockmarketstack.com/tools/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](https://stockmarketstack.com/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](https://stockmarketstack.com/tools/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.

## Where you will meet this

- [ORATS](https://stockmarketstack.com/tools/orats.md)
- [QuantLib](https://stockmarketstack.com/tools/quantlib.md)
- [Intrinio](https://stockmarketstack.com/tools/intrinio.md)
- [EODHD](https://stockmarketstack.com/tools/eodhd.md)
- [Unusual Whales](https://stockmarketstack.com/tools/unusual-whales.md)
- [AlgoSeek](https://stockmarketstack.com/tools/algoseek.md)
- [Alpaca Market Data](https://stockmarketstack.com/tools/alpaca-market-data.md)
- [AmiBroker](https://stockmarketstack.com/tools/amibroker.md)
- [Backtrader](https://stockmarketstack.com/tools/backtrader.md)
- [bt](https://stockmarketstack.com/tools/bt.md)
- [Cboe DataShop](https://stockmarketstack.com/tools/cboe-datashop.md)
- [Edgewonk](https://stockmarketstack.com/tools/edgewonk.md)

## FAQ

### Why do two providers give different greeks for the same contract?

Because each one chose a model and a set of inputs, and neither choice is published as part of the number. A different volatility input, a different interest rate curve, a different dividend assumption, a different treatment of early exercise, or a quote sampled a second apart will all move a delta. The difference is modelling, not an error in either feed.

### Can I take delta from one vendor and vega from another?

Not in the same table, no. The two numbers are partial derivatives of different model runs, so putting them side by side implies a consistency that does not exist. If a figure has to be comparable across a series or across time, compute the whole set yourself from quotes and one documented model, or take the whole set from one provider and record which.

## Sources

1. [Understanding Options Greeks](https://www.optionseducation.org/advancedconcepts/understanding-options-greeks) — The Options Industry Council, read 2026-09-21
2. [Volatility and the Greeks](https://www.optionseducation.org/advancedconcepts/volatility-the-greeks) — The Options Industry Council, read 2026-09-21
3. [Staff Accounting Bulletin Topic 14, Share-Based Payment](https://www.sec.gov/interps/account/sabcodet14.htm) — US Securities and Exchange Commission, read 2026-09-21
4. [Cboe Volatility Index Mathematics Methodology, version 5.0](https://cdn.cboe.com/resources/indices/Cboe_Volatility_Index_Mathematics_Methodology.pdf) — Cboe Global Indices, 2026-02-26

*Last updated 2026-09-21. A reference page, corrected in place — not a dated post.*