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Novel Insights in the Levy-Levy-Solomon Agent-Based Economic Market Model

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  • Maximilian Beikirch
  • Torsten Trimborn

Abstract

The Levy-Levy-Solomon model (A microscopic model of the stock market: cycles, booms, and crashes, Economic Letters 45 (1))is one of the most influential agent-based economic market models. In several publications this model has been discussed and analyzed. Especially Lux and Zschischang (Some new results on the Levy, Levy and Solomon microscopic stock market model, Physica A, 291(1-4)) have shown that the model exhibits finite-size effects. In this study we extend existing work in several directions. First, we show simulations which reveal finite-size effects of the model. Secondly, we shed light on the origin of these finite-size effects. Furthermore, we demonstrate the sensitivity of the Levy-Levy-Solomon model with respect to random numbers. Especially, we can conclude that a low-quality pseudo random number generator has a huge impact on the simulation results. Finally, we study the impact of the stopping criteria in the market clearance mechanism of the Levy-Levy-Solomon model.

Suggested Citation

  • Maximilian Beikirch & Torsten Trimborn, 2020. "Novel Insights in the Levy-Levy-Solomon Agent-Based Economic Market Model," Papers 2002.10222, arXiv.org.
    • Handle: RePEc:arx:papers:2002.10222
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    References listed on IDEAS

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    1. Egenter, E. & Lux, T. & Stauffer, D., 1999. "Finite-size effects in Monte Carlo simulations of two stock market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 268(1), pages 250-256.
    2. Torsten Trimborn & Philipp Otte & Simon Cramer & Max Beikirch & Emma Pabich & Martin Frank, 2018. "SABCEMM-A Simulator for Agent-Based Computational Economic Market Models," Papers 1801.01811, arXiv.org, revised Oct 2018.
    3. Levy, Moshe & Levy, Haim & Solomon, Sorin, 1994. "A microscopic model of the stock market : Cycles, booms, and crashes," Economics Letters, Elsevier, vol. 45(1), pages 103-111, May.
    4. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    5. R. Kohl, 1997. "The Influence of the Number of Different Stocks on the Levy–Levy–Solomon Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 8(06), pages 1309-1316.
    6. Simon Cramer & Torsten Trimborn, 2019. "Stylized Facts and Agent-Based Modeling," Papers 1912.02684, arXiv.org.
    7. Levy, Haim & Levy, Moshe & Solomon, Sorin, 2000. "Microscopic Simulation of Financial Markets," Elsevier Monographs, Elsevier, edition 1, number 9780124458901.
    8. Zschischang, Elmar & Lux, Thomas, 2001. "Some new results on the Levy, Levy and Solomon microscopic stock market model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 291(1), pages 563-573.
    9. Hellekalek, P., 1998. "Good random number generators are (not so) easy to find," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 46(5), pages 485-505.
    10. Lux, Thomas, 2008. "Stochastic behavioral asset pricing models and the stylized facts," Kiel Working Papers 1426, Kiel Institute for the World Economy (IfW Kiel).
    11. E. Samanidou & E. Zschischang & D. Stauffer & T. Lux, 2007. "Agent-based Models of Financial Markets," Papers physics/0701140, arXiv.org.
    12. Lux, Thomas, 2008. "Stochastic behavioral asset pricing models and the stylized facts," Economics Working Papers 2008-08, Christian-Albrechts-University of Kiel, Department of Economics.
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