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Is someone aware of publications that try to model limit order book (and market mircostructure) in general using CS tools (such as online machine learning, game theory ecc...) and not stochastic processes? I am aware of the work by Kearn (et al.)

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They are different trends of research

  • agent based models, and you are right: Michael is a pioneer
  • point process based models, and I would say that Frederic's book is a reference: Limit Order Books.
  • propagator initiated models, here Jean-Philippe's work, and his recent book, is what has to be read: Trades, Quotes and Prices.
  • Markov-chain based models, initiated by Rama and Adrien, and then completed by Mathieu, Weibing and CA to form the Queue Reactive model. See Market Microstructure in Practice, 2nd Edition.

You can guess that I have a preference for the latest one, but the true is that they all contain important components that are in fact difficult to maintain together in the same model:

  • fine simulation of market makers vs traders (agent-based are better)
  • mesoscopic coupling of orders sent by different agents (generic point process are better)
  • mean reversion and memory of prices (propagator are better)
  • account for the current state of the orderbook (Queue Reactive is better).

In all cases they are two mysteries to be solved

  1. the better you model tick by tick liquidity dynamics, the less you explain macroscopic volatility, probably because macroscopic volatility is generated by exogenous events, that you cannot read in the tick by tick data
  2. the square root nature of the macroscopic market impact is compatible in nature with what you will obtain at the tick by tick level (for instance with a propagator, to make it simple), but again they are not fully compatible.

If you want to play with deep neural nets, have a look at Deep Learning for Limit Order Books, by Justin Sirignano.

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I guess I could give you a far from complete, but good start of researchers who've tried using ML/CS in LOB modeling: Alvaro Cartea, Marcos Lopez de Prado, Sebastian Jaimungal, Dieter Hendricks, Brian Ning, Jean-Philippe Bouchaud (mean-field games, not ML), Rama Cont (used to only do math modeling, but recently tried deep learning for price formation), etc.

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