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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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    References listed on IDEAS

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    1. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
    2. Madhavan, Ananth & Richardson, Matthew & Roomans, Mark, 1997. "Why Do Security Prices Change? A Transaction-Level Analysis of NYSE Stocks," Review of Financial Studies, Society for Financial Studies, vol. 10(4), pages 1035-1064.
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    6. Mendelson, Haim, 1982. "Market Behavior in a Clearing House," Econometrica, Econometric Society, vol. 50(6), pages 1505-1524, November.
    7. Roll, Richard, 1984. " A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market," Journal of Finance, American Finance Association, vol. 39(4), pages 1127-1139, September.
    8. Fabrizio Lillo & J. Doyne Farmer & Rosario N. Mantegna, 2002. "Single Curve Collapse of the Price Impact Function for the New York Stock Exchange," Papers cond-mat/0207428, arXiv.org.
    9. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
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    Cited by:

    1. repec:spr:annopr:v:282:y:2019:i:1:d:10.1007_s10479-018-3019-4 is not listed on IDEAS
    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. 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.
    5. 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.
    6. 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.
    7. Shingo Ichiki & Katsuhiro Nishinari, 2014. "Simple Stochastic Order-Book Model of Swarm Behavior in Continuous Double Auction," Papers 1411.2215, arXiv.org.
    8. 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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