Gamma is a term a lot of people know about, but not a lot of people know what it does.

Let's talk about gamma pinning, and start breaking down this second order greek.

A thread (1/x)
To start, we need to know what pin risk is.

Pin risk emerges over options selling, specifically when the contracts are at or near expiration. Let's say stock XYZ is trading at $100.75, with expirations that day at $97.5, $100, and $102.5, and high OI on the $100 and $102.5 (2/x)
If Ape A is turbo long the $100 strike, the MM or option seller has to be short the $100 strike in equivalent delta w.r.t. the underlying (in this scenario probably short ~55-60 shares). (3/x)
If you didn't know, gamma is the rate of change of delta (first derivative), and measures how much delta moves with a $1 movement in the underlying.

If you did know, congrats, here's a cookie: 🍪

But why does this matter? (4/x)
Gamma increases when contracts are near expiration, and at the money, as you can see from the visual.

The closer the contract is to expiration, the more narrow the tails on the bell curve become, and you see extreme movements in gamma/delta (5/x)
Back to the pinning.

Stocks become very volatile during these expirations, so MM's try to understand where their greatest risk is. Since MM's are short quite a bit of contracts to hedge against the Apes buying 25000 1dtes on each strike, they will try and lower share price (6/x)
Given the high OI on the $100 strike call, there will most likely be high OI on the $100 put as well, but lets say instead of 25k OI there is 12.5k OI. For the put side, MM's want the stock to close at $100.01 or above, and for the call side, $99.99 or below. (7/x)
We can see that the net OI at that strike is positive 12,500, so the MM's will have more incentive to pin below $100. (8/x)
If XYZ closes that expiration cycle at $99.99, the MM's keep all the money they sold the calls for at the $100 and $102.5 strike, unless some morons try to exercise the calls when they're OTM. (don't do that, they still make money) (9/x)
So naturally, the MM's will do everything in their power to try and keep the stock below $100. This effect is known as pinning.

But falcon, you said gamma pinning.

I know, we're getting to it. (10/x)
The aforementioned system of "pinning the strike" is a functioning so the MM's/sellers can appropriately hedge risk and exposure. (11/x)
Gamma pinning, simply, is a byproduct of delta hedging. Since MM's want to remain delta neutral (re: directionally neutral), they have to target gamma. A standard gamma pin is at the strike that has the most Gamma, in our case, the $100C/$100P had a positive net gamma. (12/x)
This positive net gamma is based on the positive 12500 net OI, so the MM's will try and keep it under $100 by expiration to collect sweet premiums. You can use this to your buying/selling advantage by examining where high gamma is. (13/x)
For a real world example, let's look at AAPL's expiration for this week.

We see high OI on call side from 160 onward. It has a net OI on the 160 strike at ~21000, so this would make MM's (most likely) try to keep AAPL at 159.99. (14/x)
As always, thanks for reading. Let me know if you have any questions, and as always, feel free to slide into DM's if you want to fight me or something.

Also, none of this is advice. Do your research, and happy hunting.
Disclaimer on this, if you look hard enough, you can probably poke a hole in something I said. It was meant to be a fairly easily interpreted version of higher level options concepts, but I would love to talk about it more.

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