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I'm trying to understand how important the limit order today for NYSE, NASDAQ, Euronext and LSE.

For example, when we talk about the volume traded during the day, what share of that volume has been traded through the limit order book in those exchanges?

I googled some papers, but the situation seems to change and be different across exchanges.

My current understanding is that for the Euronext, the trading through the limit order book is central.

How big is the share of limit order book trades and what are the different options to trade?

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Every match that hits the tape from the perspective of displayed ECNs is a market order matched with a limit order. You can think of this in terms of makers and takers. If I want to buy MSFT at 51.00 and post a limit for that price 3 microseconds before you post your limit to sell at 51.00 then I am the maker and you are the taker. And your sell order will be treated as a market order unless you used some instruction that would only allow it to execute on the passive side. In that case you would wait until my order fills and someone else comes to buy at 51.00.

I'm not accounting for all of the routes and order options selected in user (or user's robot) land, because the piece that becomes visible to the ECN matching engine and gets the fill is either a limit or market order and will match against the other.

This alone would make limit orders half of the equation and that's an important level. But if I know that when I route to a particular venue there are more likely to be orders at the prices I want (they have more liquidity) then I will choose to route there more often. This is a self-reinforcing effect for liquidity, where limits want to rest there because more takers will come there and more makers come to match with more takers, etcetera. Market orders (takers) are the benefit. They're not the anchor orders of this virtuous cycle. That's why the earlier models and more popular models of maker-taker ECNs pay rebates to resting liquidity / makers (limit orders) and charge fees to takers (market orders, including marketable limits).

Matching regulations (Reg NMS - 611) are intended to change some of the analysis in the last paragraph, because the matching engines have to look at multiple venues for resting liquidity (limit orders) and match against the best prices. I think it would go to the edges of question scope to consider how business models change when shop owners have to route customers to competitors with better prices, but I could justify a place for it in a comprehensive answer. I'm leaving it alone mostly, because it's an evolving area of research where I presently only have glimmers of insight.

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Trades in the US can just go to the tape (the ADF). This is common with certain block trades and certain trades linked to derivatives. There is a flag on those trades to let you see that they are "average priced trades" or "derriv linked trades"...

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