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can you explain what is meant by 'price discreteness' in stock markets? I happened to read this term in some papers but I don't know how to define it

In the paper "Do Price Discreteness and Transactions Costs Affect Stock Returns? Comparing Ex-Dividend Pricing before and after Decimalization" https://www.jstor.org/stable/3648205 the authors state that " several microstructure theories argue that taxes are not the key factor affecting ex-day price behavior and that the price drop (relative to the dividend paid) can be explained by market frictions such as price discreteness and bid-ask spreads. What is exactly price discreteness?

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The first sentence in the abstract explains it. "By the end of January 2001, all NYSE stocks had converted their price quotations from 1/8s and 1/16s to decimals". The prices are becoming less discrete and more continuous. For example, if an original price range was like 9.000, 9.125, 9.250 ... 10.000 and then it became 9.001, 9.002, 9.003 ... 10.000, it is becoming less discrete and more continuous.

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  • $\begingroup$ thanks, I appreciate it $\endgroup$
    – XY0
    Nov 20, 2023 at 12:15
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    $\begingroup$ In any real market, prices differ by a minimum increment called a tick. You cannot bid $\pi=3.1415926 \cdots$ dollars for an item, but must choose between 3.141 and 3.142 if the tick size is 0.001. That prevents infinite bargaining where buyer and seller make closer and closer prices without ever matching each other exactly and thus never being able to transact. So prices are necessarily discrete and not continuous. $\endgroup$
    – nbbo2
    Nov 20, 2023 at 13:05
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    $\begingroup$ does this means that we cannot define price as continuos? Prices must be discrete, is this right? $\endgroup$
    – XY0
    Nov 20, 2023 at 15:50
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    $\begingroup$ In real markets prices are discrete, but for theoretical analysis we sometimes assume continuous prices as a simplification. $\endgroup$
    – nbbo2
    Nov 20, 2023 at 15:59
  • $\begingroup$ Love the first answer by @nbbo2, it is much more thorough than mine. $\endgroup$
    – KaiSqDist
    Nov 20, 2023 at 16:37

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