Order book matching: Do price quotes change when market orders are being matched?


So, as far as I'm aware, there are two ways of calculating the quote that an exchange displays for a given security. One would be to take the average between the current bid and ask spread, the other is to simply take the last price at which a bid and ask have been matched and thus generated a trade.

In the second case, all quotes would be results of trades being matched: However, I'm now wondering how exactly “supply & demand” would impact the price as is always being said? It's not like the remainder of the order book of the security impacts the price itself. Is it just by virtue of indirectly making more matches of higher and higher prices when demand exceeds supply, due to participants inputting limit orders at higher prices in those cases?


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