Abstract
Introduced in 1994, the Levy-Levy-Solomon (LLS) model developed into a standard tool to study in realistic detail the emergence of complex dynamics of stock markets with heterogeneous quasi-rational partially informed investors. We review the main features of this model and several of its extensions. We study the effects of investor heterogeneity and show that predation, competition, or symbiosis may occur between different investor populations. Many properties observed in actual markets appear as natural consequences of the LLS dynamics: truncated Lévy distribution of short-term returns, excess volatility, a “U-shape” pattern of return autocorrelation, and a positive correlation between volume and absolute returns. We also comment on the emergence of power law tails in the distribution of investor wealth and its relation to the efficient market hypothesis.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
M. Levy, H. Levy, S. Solomon: Microscopic Simulation of Financial Markets ( Academic Press, New York 2000 )
M. Levy, H. Levy, S. Solomon: Economics Letters, 45, 103 (1994); S. Moss de Oliveira, H. de Oliveira, D. Stauffer: Evolution, Money, War and Computers (B.G. Teubner, Stuttgart-Leipzig 1999); S. Solomon: ‘The microscopic representation of complex macroscopic phenomena’. In: Annual Reviews of Computational Physics II, ed. by D. Stauffer (World Scientific, Singapore 1995) pp. 243–294; S. Solomon: Comp. Phys. Comm. 121–122, 161 (1999)
T. Hellthaler: Int. J. Mod. Phys. C 6, 845 (1995); R. Kohl: Int. J. Mod. Phys. C 8, 1309 (1997)
M. Levy, H. Levy, S. Solomon: J. de Phys. I 5, 1087 (1995)
P.W. Anderson, J. Arrow, D. Pines: eds., The Economy as an Evolving Complex System ( Addison-Wesley, Redwood City 1988 )
E. Egenter, T. Lux, D. Stauffer: Physica A 268, 250 (1999)
E. Fama, K. French: J. Pol. Econ. 96, 246 (1988)
R.J. Shiller: American Economic Review, 71, 421 (1981)
M. Levy, N. Persky, S. Solomon: Int. J. High Speed Comput. 8, 93 (1996); see also J.D. Farmer: ‘Market Force, Ecology and Evolution’, e-print adaporg/9812005; and J.D. Farmer, S. Joshi: ‘Market Evolution Toward Marginal Efficiency’, SFI report 1999
M. Levy, S. Solomon: Physica A 242, 90 (1997); M. Levy: ‘Are Rich People Smarter?’ UCLA, Working Paper, 1997; M. Levy: ‘Wealth Inequality and the Distribution of Stock Returns’ Hebrew University, Working Paper, 1999
S. Solomon, M. Levy: Int. J. Mod. Phys. C 7, 745 (1996); S. Solomon: ‘Stochastic Lotka-Volterra systems of competing auto-catalytic agents lead generically to truncated Pareto power wealth distribution, truncated Levy distribution of market returns, clustered volatility, booms and crashes’. In: Computational Finance 97, ed. by A-P.N. Refenes, A.N. Burgess, J.E. Moody (Kluwer Academic Publishers, Dordrecht 1998); O. Biham, O. Malcai, M. Levy, S. Solomon, Phys Rev E 58, 1352 (1998)
M. Levy, S. Solomon: Int. J. Mod. Phys. C 7, 595 (1996)
A. Blank, S. Solomon: ‘Power Laws and Cities Population’, cond-mat/0003240
V. Pareto: Cours d’Economie Politique, Vol. 2 ( Rouge, Lausanne 1897 )
S. Solomon: ‘Generalized Lotka-Volterra (GLU) Models and Generic Emergence of Scaling Laws in Stock Markets’, in: Applications of Simulation to Social Sciences, ed. by G. Ballot and G. Weisbuch ( Hermes Science Publications, Paris 2000 )
O. Malcai, O. Biham, S. Solomon: Phys. Rev. E 60, 1299 (1999)
B.B. Mandelbrot: Comptes Rendus 232, 1638 (1951); H.A. Simon, C.P. Bonini: Amer. Econ. Rev. 48, 607 (1958); R.N. Mantegna: Physica A 179, 232 (1991); R.N. Mantegna, H.E. Stanley: Nature 376, 46 (1995)
P. Lévy: Théorie de l’Addition des Variables Aléatoires ( Gauthier-Villiers, Paris 1937 )
A.J. Lotka: Elements of Physical Biology (Williams and Wilkins, Baltimore 1925); V. Volterra: Nature 118, 558 (1926)
M.J. Gordon, G.E. Paradis, C.H. Rorke: American Economic Review 62, 107 (1972)
I. Friend, M.E. Blume: American Economic Review 65, 900 (1975)
H. Levy: J. Risk Uncert. 8, 289 (1994)
D. Kahneman, A. Tversky: Econometrica 47, 263 (1979)
W.A. Brock, C.H. Hommes: Econometrica 65, 1059 (1997)
C. Chiarella, X.Z. He: Computational Economics 19, 95 (2002)
E. Zschischang, T. Lux: Physica A 291, 563 (2001)
W.B. Arthur, J.H. Holland, B. LeBaron, R.G. Palmer, P. Taylor: ‘Asset Pricing Under Endogenous Expectations in an Artificial Stock Market’, in The Economy as an Evolving Complex System II, ed. by W.B. Arthur, S. Durlauf, D. Lane ( Addison-Wesley, Redwood City 1997 )
J.M. Poterba, L.H. Summers: J. Fin. Econom. 22, 27 (1988)
N. Jegadeesh, S. Titman: J. Fin. 48, 65 (1993)
A.B. Atkinson, A.J. Harrison: Distribution of Total Wealth in Britain ( Cambridge University Press, Cambridge 1978 )
J. Steindl: Random Processes and the Growth of Firms — A Study of the Pareto Law ( Charles Griffin & Company, London 1965 )
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Solomon, S., Levy, M. (2004). An Updated Review of the LLS Stock Market Model: Complex Market Ecology, Power Laws in Wealth Distribution and Market Returns. In: Wille, L.T. (eds) New Directions in Statistical Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08968-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-662-08968-2_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07739-5
Online ISBN: 978-3-662-08968-2
eBook Packages: Springer Book Archive