One interesting thing about "highest bid" and "lowest ask" prices is that they can sometimes move up and down for days without a transaction ever happening.
This can be observed in certain illiquid markets, e.g. for a specific bond of a company. In those cases, the "last trade price" is meaningless and it's very important to instead look at the bids and asks in the order book.
Why? Clearly, no one is actually willing to trade at those prices. Sometimes, one illogical price in illiquid markets drive the orderbook to illogical extremes. Without a transaction, all are meaningless.
Bids and asks are making bold predictions about the current value of an asset. If they are wrong then anyone can enter the market and make a profit. Bid/ask of 99.90/100.10 means that the true value of the asset is between 99.90 and 100.10, because if it was really worth $100.20 someone would come in and buy up all the offers through $100.19 (give or take a bit for risk management, fees, and minimum profit targets). Usually what happens though in these markets is that the bid/ask is $95/$105 and true value is something like $101 but no buyer wants to pay a $4 spread and no seller wants to pay a $6 spread, so no trades happen. The last price could be $90 from back when the asset was $90/$100 true value around $95 and someone really needed to get out and was willing to pay (or didn’t know).
Yeah kind of. Except market makers can pull liquidity in a microsecond and have higher privileges on many exchanges that retail investors investing through brokers do not.
The best measure if pricing in my view is "what average price would I get or slippage would I see if I sold X shares right now?"
But they _are_ willing to trade at those prices. The person who posted the highest bid is willing to buy at that price and the person who posted the lowest ask is willing to sell at that price. Both regardless of the last trade price.
The lack of "crossing" between those two doesn't mean no one is willing to trade.
The context here was the highest bid / lowest ask. The context was not orders deep in the order book. If your order is the best order available in the book, anyone can just take it, and you will not have any time to move your order before a trade is executed.
The reason I said "it's important to look at the order book" is because otherwise you might enter a market order and expect to get something near the last trade price. Which you won't.
I do think the "correct price" is near the middle of the spread though. Because this sort of thing happens not just because of illiquidity, but also because everyone involved knows what the "correct" price is. (E.g. because bonds have very predictable cash flows.) There's no difference in opinion large enough to convince a trader to cross the spread.
This can be observed in certain illiquid markets, e.g. for a specific bond of a company. In those cases, the "last trade price" is meaningless and it's very important to instead look at the bids and asks in the order book.