When a limit order is fulfilled, is it always at the specified price? In other words, is it possible that a buy (sell) order will be completed with a lower (higher) price?

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    Short answer: yes. For instance, if you place a limit order to sell your stock below the current maximum bid (i.e. the bid component of the NBBO, then your broker is legally obligated to execute your order at the current maximum bid price instead, giving you the best currently available price. Someone else can probably fill in with more details and/or citations. – Jason R May 16 '17 at 14:11

A limit order when place, matches at the limit price or better. If there are no better matches, it sits in the books. At this point in time it becomes a true limit order and does not match for better.

Related question How do exchanges match limit orders?

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