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What are different distribution models typically used for generating orderbooks under high volatility, illiquidity, and multiple exchanges with different fees?

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  • $\begingroup$ letmegpt.com/… But seriously - according to ChatGPT, answer is Zipf Distribution $\endgroup$
    – keon6
    Apr 26, 2023 at 5:37
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    $\begingroup$ I cannot completely understand what you are asking or want to achieve but essentially a snapshot of an orderbook consists of bid/ask (price) and sizes. It updates based on new information. This is a process that consists of different data that are related or not. Different levels have different meanings and purposes (a price and size at level N which is X% away from mid price can be there just for fun and get canceled as N or X reduces). If you want to generate data for simulation, you can use random walk with some drift for mid price, Poisson for update and linear or uniform for the size. $\endgroup$
    – quantinho
    Apr 26, 2023 at 7:09

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They are three levels of sophistication of order book models (there is a book on the topic: Abergel, Frédéric, Marouane Anane, Anirban Chakraborti, Aymen Jedidi, and Ioane Muni Toke. Limit order books Cambridge University Press, 2016)

  1. Zero intelligence models - Farmer, J. Doyne, Paolo Patelli, and Ilija I. Zovko. "The predictive power of zero intelligence in financial markets" Proceedings of the National Academy of Sciences 102, no. 6 (2005): 2254-2259.
  2. 2-dimension flows - Cont, Rama, and Adrien De Larrard. "Price dynamics in a Markovian limit order market" SIAM Journal on Financial Mathematics 4, no. 1 (2013): 1-25.
  3. Queue Reactive models - Huang, Weibing, C-A L, and Mathieu Rosenbaum. "Simulating and analyzing order book data: The queue-reactive model" Journal of the American Statistical Association 110, no. 509 (2015): 107-122.

In the first ones you focus on a few distributions (of order sizes, of frequency of events, etc) an univariate way and you replay them. In the second ones you focus on the trajectories of the two first queues (first bid and ask) and events that modify them. In the third ones you do the same but you condition the intensities of events by the shape of the orderbook.

The take away of this line of research (spanned over more than 10 years) is that: the intensity of events conditioned by the shape of the order book reflects well the dynamics of liquidity (Queue Reactive), but not well the macroscopic volatility (it is toon mean reverting). This is the opposite for the Zero-intelligence approach. The middle approach is interesting from a theoretical viewpoint, but you can in general do better in practice.

There is no reason to not use them in a fragmented setup (ie multiple order books), it is "just" that you will have to increase the dimension of the models.

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