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I've spoken to one or two persons at some market making shops, and I'm under the impression that for modelling tick data, aside from the rise of ML, a pure jump process such as the variance gamma model is preferred certainly over diffusion models, and sometimes even over jump-diffusion models.

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This [the use of pure jump models] does make sense to me. But I wanted to ask/check if this is indeed generally the case for the HFT business, or did I just happen to speak to an outlier in the business?

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    $\begingroup$ You question is about the practice, but for theory there is Hautch "Econometrics of Financial High-Frequency Data" (2012) with a discrete-time approach and Ait-Sahalia & Jacod "High-Frequency Financial Econometrics" (2014) with a continuous-time approach. $\endgroup$
    – Richard Hardy
    Commented Sep 30, 2023 at 16:52

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