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I've searched, but found no literature on market making in single tick markets. I'd appreciate any references.

Given that most literature on MM assumes micro-structure is mean-reverting due to the bid-ask bounce, none of this applies in the case of a single tick market since the 'mean-reversion' is a single tick.

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    $\begingroup$ Do you mean tight spread by one ticker market? bid-ask bounce is present there as well, so maybe worth explaining what you mean. $\endgroup$
    – LazyCat
    Mar 27, 2019 at 14:38
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    $\begingroup$ by definition on a futures exchange a 'tick' is the smallest possible (allowed) price increment so commonly, or potentially, all contracts can create single tick markets if the offer is one tick above the bid?? $\endgroup$
    – Attack68
    Mar 27, 2019 at 18:05
  • $\begingroup$ @LazyCat By one-tick market, I mean the spread is 99% of the time a single tick. There is indeed bid-ask bounce, but I'd hardly call that 'mean reverting' in the sense most of the literature on MM addresses $\endgroup$
    – wildbunny
    Mar 27, 2019 at 19:24
  • $\begingroup$ I believe, people usually call it tight spread (stocks or other instruments). Historically, academics studies didn't have the access to the limit order book and were tracking the price of the instrument using trade prices. These experience bid-ask bounce no matter what the spread is. More recently people started to use mid-price, which is much more stable. There is also a decent number of papers on the inventory risk. Perhaps, you can start here: quant.stackexchange.com/questions/8897/… $\endgroup$
    – LazyCat
    Mar 28, 2019 at 1:50
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    $\begingroup$ No, there are differences in MM between tight spread and wide spread instruments, but a) they have little to do with bid-ask bounce b) most academic research is applicable to both cases $\endgroup$
    – LazyCat
    Mar 28, 2019 at 12:25

2 Answers 2

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The paper you are looking for is Large tick assets: implicit spread and optimal tick size by Dayri and Mathieu Rosenbaum 2013. they explain the role of the tick in the relation between market makers and investors. In short their main measure (coming from another paper on "uncertainty bounds") is made of the number of "continuation of trade signs" divided by "alternation of trade signs": $$\eta=\frac{N^{cont}}{2N^{alt}}.$$ and they show how it can efficiently be used to complement a "one tick spread" with a measure of the implicit spread.

Later, in How to predict the consequences of a tick value change? Evidence from the Tokyo Stock Exchange pilot program, with Mathieu and Webbing Huang (2015), we have shown how it can be used to predict the impact of a tick change by exchanges (using the Japan as a use case).

And finally Mathieu again developed a theoretical framework to show how exchanges could us the tick size to balance the asymmetry of information between investors and market makers; see Optimal make-take fees for market making regulation, El Euch, Mastrolia, Rosenbaum, Touzi (2019)

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  • $\begingroup$ @wildbunny For posterity and other users' benefit, I've to say it's a weird decision that this was chosen as the answer. All three papers referenced here are about market design and what the trading venue should set as the tick size, not about market making nor mean reversion. i.e. As a market maker, you can't change the tick size at your whim - that's the exchange or ECN's decision. $\endgroup$
    – databento
    Dec 5, 2022 at 1:56
  • $\begingroup$ @rkr my view is that understanding the intrication between the tick size and the mean reversion it fosters on both sides of the book is deeply linked with market making; that's probably why the community promoted this answer as an adequate one. But in all fairness; this is more "existential" answer on market making than a technical answer to the technical implementation of market making strategies. $\endgroup$
    – lehalle
    Dec 10, 2022 at 10:40
  • $\begingroup$ I appreciate the follow-up. Don't get me wrong, I think you wrote a high quality answer, it's just that I don't think it had answered the question. $\endgroup$
    – databento
    Dec 10, 2022 at 13:03
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Instead of "mean reversion" in the classical sense, you should expect to see negative autocorrelation in the next price move: You would typically see that if it upticks (i.e. midprice goes up on next best bid or best offer level formation), it is more likely to downtick on the next price move. The next midprice change should be negatively autocorrelated.

Many still refer to this as a "mean-everting behavior", so it's really what you want to call it.

I think what you're looking for is literature on how to capture this as an alpha and the truth is that there's no free lunch because the stylized observation here is too simple:

  • The most naive reaction to this microstructural observation is to join the best bid after a downtick and vice versa.
  • However, most MMs are aware of this, so you should also expect your "desired" fill rate to be low on the best bid after a downtick, and low on the best offer after an uptick.
  • Moreover most aggressive participants are aware of this as well, so you should expect your "adverse" fill rate to be high on the best bid after a downtick, and high on the best offer after an uptick.
  • This partly shifts the focus to how you can improve your fill rate, which is a hard open problem that there's no good academic literature on: the most obvious follow-up to increase your fill rate is to layer more levels ahead of time, but then this also means your open order risk is higher and the strategy state space becomes much more complex.
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