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Non-constant rates and over-diffusive prices in a simple model of limit order markets

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  • Damien Challet
  • Robin Stinchcombe

Abstract

Using simple particle models of limit order markets, we argue that the mid-term over-diffusive price behaviour is due to the variability of market order and limit order rates. Several rules for rate changes are considered. We obtain analytical results for bid-ask spread properties, Hurst plots and price increment correlation functions.

Suggested Citation

  • Damien Challet & Robin Stinchcombe, 2003. "Non-constant rates and over-diffusive prices in a simple model of limit order markets," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 155-162.
    • Handle: RePEc:taf:quantf:v:3:y:2003:i:3:p:155-162
    DOI: 10.1088/1469-7688/3/3/301
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    2. Roberto Mota Navarro & Hern'an Larralde Ridaura, 2016. "A detailed heterogeneous agent model for a single asset financial market with trading via an order book," Papers 1601.00229, arXiv.org, revised Jul 2016.
    3. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
    4. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach to Order Book Modelling," Post-Print hal-00621253, HAL.
    5. Ichiki, Shingo & Nishinari, Katsuhiro, 2015. "Simple stochastic order-book model of swarm behavior in continuous double auction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 304-314.
    6. Alberto Ciacci & Takumi Sueshige & Hideki Takayasu & Kim Christensen & Misako Takayasu, 2020. "The microscopic relationships between triangular arbitrage and cross-currency correlations in a simple agent based model of foreign exchange markets," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    7. Maskawa, Jun-ichi, 2007. "Stock price fluctuations and the mimetic behaviors of traders," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 172-178.
    8. Maskawa, Jun-ichi, 2007. "Correlation of coming limit price with order book in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 90-95.
    9. Shingo Ichiki & Katsuhiro Nishinari, 2014. "Simple Stochastic Order-Book Model of Swarm Behavior in Continuous Double Auction," Papers 1411.2215, arXiv.org.
    10. Roberto Mota Navarro & Hernán Larralde, 2017. "A detailed heterogeneous agent model for a single asset financial market with trading via an order book," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-27, February.
    11. Johann Lussange & Stefano Vrizzi & Sacha Bourgeois-Gironde & Stefano Palminteri & Boris Gutkin, 2022. "Stock Price Formation: Precepts from a Multi-Agent Reinforcement Learning Model," Post-Print hal-03827363, HAL.
    12. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    13. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    14. Johann Lussange & Stefano Vrizzi & Sacha Bourgeois-Gironde & Stefano Palminteri & Boris Gutkin, 2023. "Stock Price Formation: Precepts from a Multi-Agent Reinforcement Learning Model," Computational Economics, Springer;Society for Computational Economics, vol. 61(4), pages 1523-1544, April.
    15. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.

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