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Exact Hurst exponent and crossover behavior in a limit order market model

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  • R. D. Willmann
  • G. M. Schuetz
  • D. Challet

Abstract

An exclusion particle model is considered as a highly simplified model of a limit order market. Its price behavior reproduces the well known crossover from over-diffusion (Hurst exponent H>1/2) to diffusion (H=1/2) when the time horizon is increased, provided that orders are allowed to be canceled. For early times a mapping to the totally asymmetric exclusion process yields the exact result H=2/3 which is in good agreement with empirical data. The underlying universality class of the exclusion process suggests some robustness of the exponent with respect to changes in the trading rules. In the crossover regime the Hurst plot has a scaling property where the bulk deposition/cancellation rate is the critical parameter. Analytical results are fully supported by numerical simulations.

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  • R. D. Willmann & G. M. Schuetz & D. Challet, 2002. "Exact Hurst exponent and crossover behavior in a limit order market model," Papers cond-mat/0206446, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0206446
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    Cited by:

    1. 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.
    2. Marc Potters & Jean-Philippe Bouchaud, 2002. "More statistical properties of order books and price impact," Science & Finance (CFM) working paper archive 0210710, Science & Finance, Capital Fund Management.
    3. 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.
    4. Jiahua Wang & Hongliang Zhu & Dongxin Li, 2018. "Price Dynamics in an Order-Driven Market with Bayesian Learning," Complexity, Hindawi, vol. 2018, pages 1-15, November.
    5. Wang, Guochao & Zheng, Shenzhou & Wang, Jun, 2019. "Complex and composite entropy fluctuation behaviors of statistical physics interacting financial model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 97-113.
    6. Shingo Ichiki & Katsuhiro Nishinari, 2014. "Simple Stochastic Order-Book Model of Swarm Behavior in Continuous Double Auction," Papers 1411.2215, arXiv.org.

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