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The put and call short, long option graphs don't seem to reflect the fact that a short call or a long put position holder could purchase the assets before maturity especially if that price is below the strike price, and gain more through the difference between that price and the price at maturity.

So is it always the case that the assets are automatically bought and sold at the maturity date(or maturity hour or maturity second)? But can it ever be perfectly simultaneous? What if there are price fluctuations between the time an asset is getting ready to be delivered and the actual moment of delivery?

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They usually delta hedge, meaning they hold the stock and bonds in relative amounts so that if the stock goes up 10 and that makes the option go up 3, they own 30% of the position in stock and 70% in bonds.

They constantly adjust this hedge so they have "no" risk.

By the time an option is about to expire, it is usually pretty far in or out of the money relative to "reasonable" short-term price moves. So what they hold is very close to what they must deliver (or not).

What is hard to appreciate is if you buy an option on 1 million of stock, they can - and do -borrow 1 million at low intermarket bank rates and put on that hedge. And, if things go really well, they end up with customers with offsetting positions that hedge themselves, at least in part.

There is a lot of detail but that is the basic idea.

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