Do MMs hedge delta with mostly stock? e.g. someone longs 50k calls at 0.2 delta, and the MM fills, do they theoretically also long 10k shares to be delta neutral? Any other common hedge instruments?

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theoretically yes they do

Yes, but they are hedging their whole balanced holding. They are making put, call and stock purchases. In rare cases they may hedge with a cohort or the market for some periods.

Market makers are making markets in many companies, some much more liquid than others. They can occasionally move the market with their hedge.

Imagine close cohorts like 2 train lines. THIS IS MEANT AS ILLUSTRATIVE, IT SN EXAMPLE. If hedging on one were to require trading say 5% of that ticket, you may see a hedge in that ticket, along with a buy or sell in the other train line to complete the hedge until a pairs trade can be made to take it all back to the original ticker.

They are fully hedged within the ticker by close of the market, but occasionally violent moves that require alternative trades to maintain order.

ETFs are occasionally hedged with futures just like other traders do. They are not exact correlaries but can serve the purpose.

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