A scaling limit for limit order books driven by hawkes processes

Ulrich Horst, Wei Xu

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Abstract

In this paper we derive a scaling limit for an infinite-dimensional limit order book model driven by Hawkes random measures. The dynamics of the incoming order flow is allowed to depend on the current market price as well as on a volume indicator. With our choice of scaling the dynamics converges to a coupled SDE-ODE system where limiting best bid and ask price processes follows a diffusion dynamics, the limiting volume density functions follows an ODE in a Hilbert space, and the limiting order arrival and cancellation intensities follow a Volterra–Fredholm integral equation.

Original languageEnglish
Pages (from-to)350-393
Number of pages44
JournalSIAM Journal on Financial Mathematics
Volume10
Issue number2
DOIs
Publication statusPublished - 2019
Externally publishedYes

Keywords

  • Hawkes processes
  • Limit order books
  • Scaling limit

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Horst, U., & Xu, W. (2019). A scaling limit for limit order books driven by hawkes processes. SIAM Journal on Financial Mathematics, 10(2), 350-393. https://doi.org/10.1137/17M1148682