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I need some assistance in understanding the relation between the "bid-ask bounce" and "the tick rule" + "quote rule".

The two rules mentioned above are used to classify the trade direction of executed trades based on data, i.e. "buy" or "sell". Here are the definitions of the two rules:

"Quote rule": You have a Ask and Bid price for a stock, and then you have a midquote which is: (Ask+Bid)/2=midquote. According to this rule you look at whether the trade price is above, beyond or at the midqoute. If the price is above, you classify the transaction as a "Buy", if below "Sell" and if the transaction price is at the midqoute a second rule has to determine the trade classification.

"Tick rule": This rule classifies a trade as buyer-initiated (Buy) if the trade price is above the preceding trade price (an uptick trade) and as seller-initiated (Sell) if the trade price is below the preceding trade price (a downtick trade). If the trade price is the same as the previous trade price (a zero-tick trade), the rule looks for the closest prior price that differs from the current trade price. Zero-uptick trades are classified as buys, and zero-downtick trades are classified as sells.

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    $\begingroup$ Please do not delete useful information from your question. It should be understandable to readers. $\endgroup$
    – nbbo2
    Jun 9, 2022 at 10:14

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The bid ask bounce is a phenomenon that you observe when you look at transaction prices in a quote driven market. Because buys and sells occur randomly, the price of the last trade changes randomly between the quoted ask and the quoted bid, this constant up and down movement is called the bid-ask bounce. For a simple example if the underlying value of the shares remains the same you could observe transaction prices 10.0 10.5 10.5 10.0 10.5 10.0 10.0 10.0 ... . The 10.0 values are sales by a customer to the market maker at the bid price and the values 10.5 are the buys by a customer from the market maker at the ask price. In general the value of the shares (the midprice) is not constant and so after a while you might see 10.5 11.0 10.5 11.0 11.0 which means that the underlyig price went up by 1.0 and the bid-ask remains 0.5. In general the bid-ask bounce is superimposed on price movement caused by supply and demand.

What can we do with this knowledge? Researchers have devised rules to extract useful information from the transaction price sequence. For example as we did above we can (try to) identify the buys and the sells, we can estimate the size of the bid ask spread, etc. The rules are not perfect, they are only heuristics, because they can be misled by some price movements (for example if the price jumps from 10.0 to 20.0 can we conclude that the bid-ask is 20-10 = 10 ? Probably not, this big price jump is probably caused by a price change and not by the bid ask bounce. Nevertheless the rules work in a majority of the cases. The different rules give slightly different results and rely on slightly different features of the observed data. They work (to the extent they do) because of the rapid bid-ask bounce.

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