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I've been reading up on market microstructure models and toyed around with them -- i.e., I got simulations for Roll (1984), Glosten-Milgrom (1985), Kyle (1985), Kyle (1985) with multiple periods.

I am wondering, though, what are some current problems in the field?

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  • $\begingroup$ Those sources are from a long time ago. It would be good to pick up a recent issue of Quantitative finance and go for the microstructure topics to get an idea of recent trends before asking this question since each article contains a literature review providing the build-up for the selected topic $\endgroup$
    – develarist
    Commented Nov 26, 2020 at 7:29
  • $\begingroup$ No expert on market infrastructure, but I believe there's still no satisfying explanation to the square root law of market impact, is it? $\endgroup$
    – Daneel Olivaw
    Commented Nov 26, 2020 at 9:19
  • $\begingroup$ Not my field either, but remember seeing a lot of papers on the effects of HFT during the past years. $\endgroup$
    – fes
    Commented Nov 26, 2020 at 9:54
  • $\begingroup$ @DaneelOlivaw I am no expert either, but recall seeing this paper which may answer the question you refer to arxiv.org/pdf/1805.07134.pdf $\endgroup$
    – d_797
    Commented Dec 26, 2020 at 17:59
  • $\begingroup$ Roll, Kyle, Glosten-Milgrom etc. are focussed on the spread and adverse selection. The area has moved on to modeling and explaining the stylized facts of price formation. The area is split into Agent based models and physics based models. I would recommend reading survey papers by Gould et al as well as the Survey paper by Parlour and Sepi. $\endgroup$
    – Ramesh Kadambi
    Commented Oct 10, 2021 at 11:22

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They are a lot of open problems in market microstructure. To have an idea of the whole landscape, have a look at Market Microstructure in Practice, 2nd Edition, by L and Laruelle.

I would split them in

  • From the viewpoint of exchanges
  1. Optimal fee schedules to "attract" liquidity (and hence efficient market makers), have a look at Optimal make-take fees for market making regulation, by El Euch, Mastrolia, Rosenbaum and Touzi.
  2. Best auction system to have more informed trading and less noise contributing to the price formation Optimal Auction Duration: A Price Formation Viewpoint, by Jusselin, Mastrolia and Rosenbaum.
  • From the perspective of asset managers
  1. Trading costs of investment strategies: is there a "saturation" effect coming from crowding, contibuting to killing an "anomaly" one invest on, have a look at Stock Market Liquidity and the Trading Costs of Asset Pricing Anomalies, by Briere, L, Tamara Nefedova and Raboun.
  2. there is a remaining puzzle on market impact: how to reconciliate high frequency price impact models and market impact of metaorders, a typical reference is Market impacts and the life cycle of investors orders, by Bacry, Iuga, Lasnier, and L.
  • From the perspective of traders and market makers
  1. Optimal trading with signals and price impact decay, the way a high frequency signal and your actual trading mix is difficult to model, and hence the optimal way to split your intensions to take a maximal profit of your information is not known. Have a look at Incorporating Signals into Optimal Trading, by L and Neuman for a tentative modeling.
  2. Optimizing cross-impact: when you have to execute a basket of orders (or if you make the market on more than one tradable instrument), how to intricate your actions optimally. Two references:
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  • $\begingroup$ Thanks a lot for the references and summary. I will keep reading. $\endgroup$
    – Stéphane
    Commented Dec 27, 2020 at 4:52
  • $\begingroup$ Really nice answer Charles $\endgroup$
    – G dos Reis
    Commented May 26, 2021 at 10:49
  • $\begingroup$ @lehalle Thank you, this is excellent. From the point of view of modeling limit order book dynamics and explaining stylized facts. What are some of the open problems? I am a student that is interested in LOB dynamics research and is looking for a PhD level problem. $\endgroup$
    – Ramesh Kadambi
    Commented Oct 10, 2021 at 11:18

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