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Understanding agent-based models of financial markets: a bottom-up approach based on order parameters and phase diagrams

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  • Ribin Lye
  • James Peng Lung Tan
  • Siew Ann Cheong
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    Abstract

    We describe a bottom-up framework, based on the identification of appropriate order parameters and determination of phase diagrams, for understanding progressively refined agent-based models and simulations of financial markets. We illustrate this framework by starting with a deterministic toy model, whereby $N$ independent traders buy and sell $M$ stocks through an order book that acts as a clearing house. The price of a stock increases whenever it is bought and decreases whenever it is sold. Price changes are updated by the order book before the next transaction takes place. In this deterministic model, all traders based their buy decisions on a call utility function, and all their sell decisions on a put utility function. We then make the agent-based model more realistic, by either having a fraction $f_b$ of traders buy a random stock on offer, or a fraction $f_s$ of traders sell a random stock in their portfolio. Based on our simulations, we find that it is possible to identify useful order parameters from the steady-state price distributions of all three models. Using these order parameters as a guide, we find three phases: (i) the dead market; (ii) the boom market; and (iii) the jammed market in the the phase diagram of the deterministic model. Comparing the phase diagrams of the stochastic models against that of the deterministic model, we realize that the primary effect of stochasticity is to eliminate the dead market phase.

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    File URL: http://arxiv.org/pdf/1202.0606
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1202.0606.

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    Date of creation: Feb 2012
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    Handle: RePEc:arx:papers:1202.0606

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    1. Lux, T. & M. Marchesi, . "Scaling and Criticality in a Stochastic Multi-Agent Model of a Financial Market," Discussion Paper Serie B 438, University of Bonn, Germany, revised Jul 1998.
    2. Giulia Iori, 1999. "A microsimulation of traders activity in the stock market: the role of heterogeneity, agents' interactions and trade frictions," Finance 9905005, EconWPA.
    3. Giardina, Irene & Bouchaud, Jean-Philippe, 2003. "Volatility clustering in agent based market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 6-16.
    4. P. Bak & M. Paczuski & M. Shubik, 1996. "Price Variations in a Stock Market with Many Agents," Working Papers 96-09-075, Santa Fe Institute.
    5. Maslov, Sergei, 2000. "Simple model of a limit order-driven market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 571-578.
    6. Marco Raberto & Silvano Cincotti & Sergio M. Focardi & Michele Marchesi, 2001. "Agent-based simulation of a financial market," Papers cond-mat/0103600, arXiv.org, revised Mar 2001.
    7. Lux, T. & M. Marchesi, . "Volatility Clustering in Financial Markets: A Micro-Simulation of Interacting Agents," Discussion Paper Serie B 437, University of Bonn, Germany, revised Jul 1998.
    8. L. Gauvin & J. Vannimenus & J.-P. Nadal, 2009. "Phase diagram of a Schelling segregation model," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 70(2), pages 293-304, July.
    9. Sato, Aki-Hiro & Takayasu, Hideki, 1998. "Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 231-252.
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