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General Semi-Markov Model for Limit Order Books: Theory, Implementation and Numerics

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  • Anatoliy Swishchuk
  • Katharina Cera
  • Julia Schmidt
  • Tyler Hofmeister

Abstract

The paper considers a general semi-Markov model for Limit Order Books with two states, which incorporates price changes that are not fixed to one tick. Furthermore, we introduce an even more general case of the semi-Markov model for LimitOrder Books that incorporates an arbitrary number of states for the price changes. For both cases the justifications, diffusion limits, implementations and numerical results are presented for different Limit Order Book data: Apple, Amazon, Google, Microsoft, Intel on 2012/06/21 and Cisco, Facebook, Intel, Liberty Global, Liberty Interactive, Microsoft, Vodafone from 2014/11/03 to 2014/11/07.

Suggested Citation

  • Anatoliy Swishchuk & Katharina Cera & Julia Schmidt & Tyler Hofmeister, 2016. "General Semi-Markov Model for Limit Order Books: Theory, Implementation and Numerics," Papers 1608.05060, arXiv.org.
    • Handle: RePEc:arx:papers:1608.05060
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    References listed on IDEAS

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    1. Rama Cont & Adrien de Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    2. Rama Cont & Sasha Stoikov & Rishi Talreja, 2010. "A Stochastic Model for Order Book Dynamics," Operations Research, INFORMS, vol. 58(3), pages 549-563, June.
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    Cited by:

    1. Jonathan A. Ch'avez-Casillas & Robert J. Elliott & Bruno R'emillard & Anatoliy V. Swishchuk, 2017. "A level-1 Limit Order book with time dependent arrival rates," Papers 1704.06572, arXiv.org.
    2. Myles Sjogren & Timothy DeLise, 2021. "General Compound Hawkes Processes for Mid-Price Prediction," Papers 2110.07075, arXiv.org.
    3. Jonathan A. Chávez-Casillas & Robert J. Elliott & Bruno Rémillard & Anatoliy V. Swishchuk, 2019. "A Level-1 Limit Order Book with Time Dependent Arrival Rates," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 699-719, September.

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