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Exchanges will usually list greeks along with the option, for example this SPX call on the CBOE: SPX241220C04000000

But how does the exchange calculate these greeks? I can think of a few ways to do so:

  • Use the "instantaneous" values of the most recent trades (minimum number to numerically compute the derivative)
  • Fit a hyperplane through a predefined amount of samples (say, minutes? hours? days? of time)
  • Fit the entire trade history to a model (e.g., B-S), and derive the greeks from the model

Presently I'm primarily interested in delta and theta, and I'm wondering how much I can "trust" the greeks to predict the long-term (~months) behaviour of the option price.
If the greeks are "instantaneous" values, then they would be extremely noisy and useless for my purposes. But if they are derived from the long-term history of the option, then it would be much more reliable for me

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    $\begingroup$ Greeks do not predict the behaviour of an option. $\endgroup$
    – amdopt
    Sep 10, 2023 at 13:26
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    $\begingroup$ These greeks, for sure, are not based on any long- or short-term history of anything. Perhaps you are confusing them with some historical calculations - correlations (also labeled rho), volalility, beta, etc. $\endgroup$ Sep 10, 2023 at 13:52
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    $\begingroup$ It seems like OP doesn't know anything about greeks in Black-Scholes model so I'm voting to close it as a basic financial question. $\endgroup$
    – Hasek
    Sep 10, 2023 at 16:05
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    $\begingroup$ Overview: (0) A model is chosen, such as the Black Scholes Merton model, (1) the unknown parameter(s) in the model, in this case $\sigma$ (volatility) is/are adjusted until the model price matches the market price (2) the Delta, Gamma, Theta etc produced by the model for this value of $\sigma$ are displayed on the CBOE web site. $\endgroup$
    – nbbo2
    Sep 10, 2023 at 16:26
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    $\begingroup$ If the answer and Wikipedia link I provided isn't enough, there is money SE for basic financial questions but if you just read any option book you should understand how Greeks are computed. The risk free rate comes from swap curves, dividend yield can also be derived (from dividend schedules consisting of declared dividends with dates and amounts and forecasts afterwards for example), and IV is simply what you solve the market price for. $\endgroup$
    – AKdemy
    Sep 10, 2023 at 16:34

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