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am trying to simulate the SFGK model from the paper "Statistical theory of the Continuous Double Auction", Eric Smith, J. Doyne Farmer, Laszlo Gillemot and Supriya Krishnamurthy [1].

The model simulates the Limit order book for various parameter values. The arrival processes are assumed to be poisson. The simulations are carried out for a limiting value of the tick size which is zero. However, zero tick size would mean the entire real line. I am uncertain as to how one simulates poisson processes for the entire line. That is essentially the issue. If we do chose a finite set of values with the tick size being non-zero. Then how are the different tick sizes different? They really can be scaled version of unit tick size. I am trying to get information on how to go from finite tick sizes to the zero tick size limit.

[1] https://arxiv.org/abs/cond-mat/0210475

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    $\begingroup$ Pls provide more details in regards to your question so that someone can understand and answer it in case the link you have provided is broken or the material is changed. $\endgroup$
    – Alper
    Mar 13, 2023 at 8:48
  • $\begingroup$ @Alper The question is directed to someone that perhaps has already seen the model. If you read the question and you do not understand it, it is unlikely that additional information will help. There is all the information you need to answer the question. I am hoping that it will be seen by someone that understands the model. $\endgroup$ Mar 14, 2023 at 0:23

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The solution is really much simpler than I realized. This is fairly simple to simulate really. I just wanted to post an answer for folks if interested. The idea here is to use a uniform distribution [-L,L]. Once you get the number you bucket it to a price level based on where it falls. Divide the range [-L,L] in tick sizes and you can let that tick size go to zero. The only thing that will change is the number of levels in the range [-L,L]. So the number of levels will be 2L/tick size. The prices inside the spread are not bucketed, keep them as is or allow for finer levels of pricing inside the spread. I will let the moderators decide if this is even useful to keep around or the post should be entirely deleted.

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  • $\begingroup$ No need to delete anything and thank you for sharing your insight. $\endgroup$
    – Bob Jansen
    Mar 16, 2023 at 11:48

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