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When european stock options have very little time until expiration (less than 2-3 hours), they can exhibit extreme sensitivity to changes in the underlying asset's price. This behavior leads to extremely high volatility values and potentially absurd Greek values.

This phenomenon occurs because option pricing models (like the Black-Scholes model) assume certain conditions, including constant volatility over the option's lifespan. As the time to expiration decreases, the option's sensitivity to changes in the underlying asset's price becomes exaggerated.

In this case, what should be the approach for volatility and greeks calculations?

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    $\begingroup$ I'd think that for very shortdated options, greeks don't make sense anymore. You will either have to fully trade the underlying (delta = 1) or not (delta = 0). $\endgroup$ Nov 8, 2023 at 7:56
  • $\begingroup$ How to manage a portfolio of options then? $\endgroup$
    – shoonya
    Nov 8, 2023 at 8:32
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    $\begingroup$ You make calls on where the underlying will be at the cut and trade accordingly. You can get really technical with a fancy jump model for 0d options but that only really helps with pricing, at the end of the day you have to take a view and trade the risk of your book and pinning risk is one of those in an option book. $\endgroup$
    – river_rat
    Nov 9, 2023 at 7:50
  • $\begingroup$ How does one get sensible greeks and implied vol estimates $\endgroup$
    – shoonya
    Nov 10, 2023 at 7:06

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You don't. The problem is that when the time horizon is so small, if the options isn't perfectly ATM, the gamma and vega $\approx0$, and delta $\approx1$. A small shift in the underlying further OTM/ITM, pushes the greeks further to 0. You can calculate the implied vol, but at the end of the day you have to convert back to dollars, where these options should be worth fractions of a cent. Further, it becomes a pointless task because you're probably going to run into computer precision problems anyway.

It's why selling 0 DTE options can be profitable. The bid-ask can be \$0.05-\$0.10, but in reality, these options should be \$0.0001.

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0DTE options don't expire on market close (i.e 4PM) but the settlement happens in after market hours. If the market is pricing a move in that time your greeks will be useless, you can adjust for that but unless you are with a very sophisticated options trading firm you cannot leave your positions after close and expect to not shit the bed.

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