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Pure-Jump Models for Tick-by-Tick and High-Frequency Data

Article Quant Q&A · Author: Frido
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Summary

The document raises a modeling question about tick-by-tick and high-frequency market data, especially in market making. It asks whether practitioners generally favor pure-jump processes, such as the variance gamma model, over diffusion models and sometimes over jump-diffusion models. The motivation is an informal impression gathered from conversations with people at market-making firms, alongside the observation that machine learning is also increasingly used.

No answer, evidence, or comparison is provided, so the document does not establish an industry-wide preference or explain when one process may outperform another. It is best read as a prompt for investigation into model choice for high-frequency data. Any conclusion would require evidence about the specific markets, data characteristics, and modeling objectives; the question alone cannot determine whether the reported practice is typical.

Key ideas

  • The document asks whether pure-jump processes are commonly used for tick-level and high-frequency data.
  • Variance gamma is given as an example of a pure-jump model.
  • The question compares pure-jump processes with diffusion and jump-diffusion approaches.
  • The stated impression comes from a small number of informal industry conversations, with no supporting evidence or answer.

Tags

High-frequency tradingMarket microstructureStatistics
Full text
# Models for tick-by-tick / high-frequency data


# Models for tick-by-tick / high-frequency data












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.

Question:

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.