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Let's say there's a stock trading at $100 and you sell a PUT for $80 that expires the coming Friday. The stock drops to $75 by Tuesday.

When are you actually forced to buy the stock? Does the option have to reach expiration date? Does the broker decide who they want to force executions on or is the very specific buyer of that option (and only them) the deciding factor?

I currently hold a PUT option that is ITM for whomever bought it, and yet it has not been exercised and I'm not sure how/when or who makes the decision on exercising that option.

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The owner of an American option (stocks and ETFs) has the right to exercise it any time before expiration.

If an option has remaining time premium, exercising it will throw away the time premium. For that reason, about 70% of options are closed early rather than exercised.

In-the-money options close to expiration often trade for a discount (the bid is less than the intrinsic value). If the owner sells at that inferior price, the market maker will do a discount arbitrage to realize the difference (short the stock and exercise the call OR buy the stock and exercise the put). This results in an option seller being assigned.

A pending dividend can also precipitate early assignment. If the time premium of an ITM put is less than the amount of the dividend, there's a dividend arbitrage available. The put and the stock are bought and the put is exercised on the ex-dividend date, capturing the difference (and the put writer is assigned early).

Last of all, ITM options are exercised by the Option Clearing Corp at expiration.

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