When an option seller is required to fulfill the contract because the buyer exercises; the event that converts a short option into a stock position.
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Assignment is the event where an option seller is required to fulfill the contract because the buyer exercises their right. For a short put it means buying the stock at the strike; for a short call it means delivering the stock at the strike. Assignment risk rises as an option moves in-the-money and concentrates near expiration, especially around ex-dividend dates for calls. See Assignment & Rolling 101.