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Switching rates and the asymptotic behavior of herding models

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  • Irle, Albrecht
  • Kauschke, Jonas
  • Lux, Thomas
  • Milaković, Mishael

Abstract

Markov chains have experienced a surge of economic interest in the form of behavioral agent-based models that aim at explaining the statistical regularities of financial returns. We review some of the relevant mathematical facts and show how they apply to agent-based herding models, with the particular goal of establishing their asymptotic behavior because several studies have pointed out that the ability of such models to reproduce the stylized facts hinges crucially on the size of the agent population (typically denoted by n), a phenomenon that is also known as n-dependence. Our main finding is that n-(in)dependence traces back to both the topology and the velocity of information transmission among heterogeneous financial agents.

Suggested Citation

  • Irle, Albrecht & Kauschke, Jonas & Lux, Thomas & Milaković, Mishael, 2010. "Switching rates and the asymptotic behavior of herding models," Kiel Working Papers 1595, Kiel Institute for the World Economy (IfW Kiel).
    • Handle: RePEc:zbw:ifwkwp:1595
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    References listed on IDEAS

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    1. Schütz, Gunter M. & de Almeida Prado, Fernando Pigeard & Harris, Rosemary J. & Belitsky, Vladimir, 2009. "Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4126-4144.
    2. Kirman Alan & Teyssière Gilles, 2002. "Microeconomic Models for Long Memory in the Volatility of Financial Time Series," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 5(4), pages 1-23, January.
    3. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 137-156.
    4. Aoki, Masanao, 2008. "Thermodynamic limits of macroeconomic or financial models: One- and two-parameter Poisson-Dirichlet models," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 66-84, January.
    5. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 261-268, July.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. Alfarano, Simone & Lux, Thomas, 2007. "A Noise Trader Model As A Generator Of Apparent Financial Power Laws And Long Memory," Macroeconomic Dynamics, Cambridge University Press, vol. 11(S1), pages 80-101, November.
    8. Alfarano, Simone & Milaković, Mishael & Raddant, Matthias, 2009. "Network hierarchy in Kirman's ant model: fund investment can create systemic risk," Economics Working Papers 2009-09, Christian-Albrechts-University of Kiel, Department of Economics.
    9. Alfarano, Simone & Milakovic, Mishael, 2009. "Network structure and N-dependence in agent-based herding models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 78-92, January.
    10. Aoki,Masanao, 1998. "New Approaches to Macroeconomic Modeling," Cambridge Books, Cambridge University Press, number 9780521637695.
    11. Lobato, Ignacio N & Savin, N E, 1998. "Real and Spurious Long-Memory Properties of Stock-Market Data: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 280-283, July.
    12. Parameswaran Gopikrishnan & Martin Meyer & Luis A Nunes Amaral & H Eugene Stanley, 1998. "Inverse Cubic Law for the Probability Distribution of Stock Price Variations," Papers cond-mat/9803374, arXiv.org, revised May 1998.
    13. Gunter M. Schutz & Fernando Pigeard de Almeida Prado & Rosemary J. Harris & Vladimir Belitsky, 2007. "Short-time behaviour of demand and price viewed through an exactly solvable model for heterogeneous interacting market agents," Papers 0801.0003, arXiv.org, revised Jun 2009.
    14. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
    15. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
    16. P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 3(2), pages 139-140, July.
    17. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 19-49, August.
    18. 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.
    19. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
    20. Follmer, Hans & Horst, Ulrich & Kirman, Alan, 2005. "Equilibria in financial markets with heterogeneous agents: a probabilistic perspective," Journal of Mathematical Economics, Elsevier, vol. 41(1-2), pages 123-155, February.
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    Cited by:

    1. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    2. S. Alfarano & M. Milakovic & M. Raddant, 2013. "A note on institutional hierarchy and volatility in financial markets," The European Journal of Finance, Taylor & Francis Journals, vol. 19(6), pages 449-465, July.

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    More about this item

    Keywords

    Markov chains; agent-based finance; herding; N-dependence;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation
    • G19 - Financial Economics - - General Financial Markets - - - Other

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