The European Physical Journal Special Topics

, Volume 225, Issue 17–18, pp 3243–3254 | Cite as

Financial price dynamics and agent-based models as inspired by Benoit Mandelbrot

Regular Article
Part of the following topical collections:
  1. Discussion and Debate: Can Economics be a Physical Science?


This short note draws some connections between Mandelbrot‗s empirical legacy, and the interdisciplinary work that followed in finance. Much of this work is now labeled econophysics, but some has always been more in the realm of economics than physics. In a few areas the overlap is even becoming quite complete as in market microstructure. I will also give some ideas about the various successes and failures in this area, and some directions for the future of agent- based modeling in particular.


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  1. 1.
    K. Adam, A. Marcet, J. Monetary Econ. (2016) forthcomingGoogle Scholar
  2. 2.
    S. Alfarano, T. Lux, F. Wagner, Comput. Econ. 26, 19 (2005)CrossRefGoogle Scholar
  3. 3.
    V. Alfi, M. Cristelli, L. Pietronero, A. Zaccaria, Eur. Phys. J. B 67, 399 (2009)ADSCrossRefGoogle Scholar
  4. 4.
    T.G. Andersen, T. Bollerslev, F.X. Diebold, P. Labys, Econometrica 96, 579 (2003)CrossRefGoogle Scholar
  5. 5.
    M. Anufriev, P. Dindo, J. Econ. Behavior and Organization 73, 327 (2010)CrossRefGoogle Scholar
  6. 6.
    W.B. Arthur, Am. Econ. Rev. 84, 406 (1994)Google Scholar
  7. 7.
    W.B. Arthur, J. Holland, B. LeBaron, R. Palmer, P. Tayler, Asset Pricing Under Endogenous Expectations in an Artificial Stock Market, in W.B. Arthur, S. Durlauf, D. Lane, editors, The Economy as an Evolving Complex System II (Addison-Wesley, Reading, MA, 1997), pp. 15–44Google Scholar
  8. 8.
    O.E. Barndorff-Nielsen, N. Shephard, J. Fin. Econometrics 2, 1 (2004)CrossRefGoogle Scholar
  9. 9.
    S. Battiston, J.D. Farmer, A. Flache, D. Garlaschelli, A.G. Haldane, H. Heesterbeek, C. Hommes, C. Jaeger, R. May, M. Scheffer, Science 351, 818 (2016)ADSCrossRefGoogle Scholar
  10. 10.
    A. Beltratti, S. Margarita, P. Terna, Neural Networks for Economic and Financial Modeling (International Thomson Computer Press, London, UK, 1996)Google Scholar
  11. 11.
    F. Black, Studies of Stock Price Volatility Changes, in Proceedings of the American Statistical Association, Business and Economics Statistics Section, 1976, pp. 177–181Google Scholar
  12. 12.
    A. Blekherman, Int. J. Bridge Eng. 3, 1 (2015)Google Scholar
  13. 13.
    T. Bollerslev, Rev. Econ. Stat. 69, 542 (1987)CrossRefGoogle Scholar
  14. 14.
    H.P. Boswijk, C.H. Hommes, S. Manzan, J. Econ. Dyn. Control 31, 1938 (2007)CrossRefGoogle Scholar
  15. 15.
    G. Bottazzi, P. Dindo, J. Econ. Dyn. Control 48, 121 (2014)CrossRefGoogle Scholar
  16. 16.
    J.P. Bouchaud, R. Cont, Macroecon. Dyn. 4, 170 (2000)Google Scholar
  17. 17.
    J.P. Bouchaud, I. Giardina, M. Mezard, Quant. Fin. 1, 212 (2001)CrossRefGoogle Scholar
  18. 18.
    J.-P. Bouchaud, J. Stat. Phys. 151, 567 (2013)ADSCrossRefGoogle Scholar
  19. 19.
    J.-P. Bouchaud, J.D. Farmer, F. Lillo, How Markets Slowly Digest Changes in Supply and demand, in Handbook of Financial Markets: Dynamics and Evolution, (North-Holland, 2009), pp. 57–160Google Scholar
  20. 20.
    J.-P. Bouchaud, P. Krueger, A. Landler, D. Thesmar, Stick Expectations and Stock Market Anomalies, Technical report, HEC, Paris, 2016Google Scholar
  21. 21.
    W.A. Brock, C.H. Hommes, J. Econ. Dyn. Control 22, 1235 (1998)CrossRefGoogle Scholar
  22. 22.
    A. Chakraborti, I.M. Toke, M. Patriarca, F. Abergel, Quant. Fin. 11, 991 (2011)MathSciNetCrossRefGoogle Scholar
  23. 23.
    D. Challet, A. Chessa, M. Marsili, Y.-C. Zhang, Quant. Fin. 1, 168 (2001)MathSciNetCrossRefGoogle Scholar
  24. 24.
    D. Challet, M. Marsili, Y.C. Zhang, Minority Games (Oxford University Press, 2004)Google Scholar
  25. 25.
    S.-H. Chen, C.-H. Yeh, J. Econ. Dyn. Control 25, 363 (2001)CrossRefGoogle Scholar
  26. 26.
    C. Chiarella, R. Dieci, X.-Z. He, Heterogeneity, Market Mechanisms, and Asset Price Dynamics, in T. Hens and K. R. Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution (Elsevier, USA, 2009), pp. 277–344Google Scholar
  27. 27.
    C. Chiarella, G. Iori, Quant. Fin. 2, 346 (2002)CrossRefGoogle Scholar
  28. 28.
    P. Cizeau, Y. Liu, M. Meyer, C.K. Peng, H.E. Stanley, Physica A 245, 441 (1997)ADSCrossRefGoogle Scholar
  29. 29.
    A. Clauset, C.R. Shalizi, M.E.J. Newman, SIAM Rev. 51, 661 (2009)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    K.J. Cohen, S.F. Maier, R.A. Schwartz, D.K. Whitcomb, Simulation 41, 181 (1983)CrossRefGoogle Scholar
  31. 31.
    R. Cont, IEEE Signal Processing Magazine 28, 16 (2011)CrossRefGoogle Scholar
  32. 32.
    R. Cont, S. Stoikov, R. Talreja, Operations Res. 58, 549 (2010)MathSciNetCrossRefGoogle Scholar
  33. 33.
    P. Cootner, editor, The Random Character of Stock Market Prices (MIT Press, Cambridge, 1964)Google Scholar
  34. 34.
    M.M. Dacorogna, R. Gencay, U.A. Muller, R.B. Olsen, O.V. Pictet, An Introduction to High-Frequency Finance (Academic Press, San Diego, CA, 2001)Google Scholar
  35. 35.
    J. Danielsson, K. James, M. Valenzuela, I. Zer, J. Fin. Stability (2016) forthcomingGoogle Scholar
  36. 36.
    V. Darley, A.V. Outkin, A NASDAQ Market Simulation, Complex Systems and Interdisciplinary Science (World Scientific, 2007)Google Scholar
  37. 37.
    Z. Ding, C.W.J. Granger, R.F. Engle, J. Empir. Fin. 1, 83 (1993)CrossRefGoogle Scholar
  38. 38.
    J. Donier, J.-P. Bouchaud, PLOS One 10, e0139356 (2015)CrossRefGoogle Scholar
  39. 39.
    E. Egenter, T. Lux, D. Stauffer, Physica A 268, 250 (1999)ADSCrossRefGoogle Scholar
  40. 40.
    P. Embrechts, C. Kluppelberg, T. Mikosch, Modeling Extremal Events for Insurance and Finance (Springer-Verlag, 1997)Google Scholar
  41. 41.
    R.F. Engle, Econometrica 50, 987 (1982)MathSciNetCrossRefGoogle Scholar
  42. 42.
    J. Estrada, J. Investing 17, 20 (2008)CrossRefGoogle Scholar
  43. 43.
    I.V. Evstigneev, T. Hens, K.R.S. -Hoppe, Evolutionary finance, in Thorsten Hens and Klaus Reiner Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution, Handbooks in Finance (North-Holland, Amsterdam, the Netherlands, 2009), pp. 509–564Google Scholar
  44. 44.
    A. Fabretti, J. Econ. Interactions and Coordination 8, 277 (2013)CrossRefGoogle Scholar
  45. 45.
    E.F. Fama, J. Business 36, 420 (1963)CrossRefGoogle Scholar
  46. 46.
    J.D. Farmer, Industrial and Corporate Change 11, 895 (2002)CrossRefGoogle Scholar
  47. 47.
    J.D. Farmer, S. Joshi, J. Econ. Behavior and Organization 49, 149 (2002)CrossRefGoogle Scholar
  48. 48.
    J.D. Farmer, L. Gillemot, F. Lillo, S. Mike, A. Sen, Quant. Fin. 4, 383 (2004)CrossRefGoogle Scholar
  49. 49.
    J.D. Farmer, P. Patelli, I. Zovko, Proc. Natl. Acad. Sci. U.S.A. 102, 2254 (2005)ADSCrossRefGoogle Scholar
  50. 50.
    A. Gaunersdorfer, C. Hommes, A Nonlinear Structural Model for Volatility Clustering, in A. Kirman and G. Teyssiere, editors, Micro Economic Models for Long Memory in Economics (Springer-Verlag, 2007), pp. 265–288Google Scholar
  51. 51.
    J. Geanakoplos, R. Axtell, D. Farmer, P. Howwitt, B. Conlee, J. Goldstein, M. Hendrey, N. Palmer, C.-Yi Yang, Am. Econ. Rev. 102, 1 (2012)CrossRefGoogle Scholar
  52. 52.
    C. Gershenson, D. Helbing, Compexity 21, 9 (2015)CrossRefGoogle Scholar
  53. 53.
    J. Geweke, Inferences and Forecasting for Deterministic Non-linear Time Series Observed With Measurement Error, in R.H. Day and P. Chen, editors, Nonlinear Dynamics and Evolutionary Dynamics (Oxford University Press, 1993)Google Scholar
  54. 54.
    F. Ghoulmie, R. Cont, J.-P. Nadal, J. Phys.: Condens. Matter 17, 1259 (2005)ADSGoogle Scholar
  55. 55.
    R. Goettler, C.A. Parlour, U. Rajan. J. Fin. 60, 2149 (2005)CrossRefGoogle Scholar
  56. 56.
    C.R. Harvey, Y. Liu, H. Zhu, Rev. Fin. Studies 29, 5 (2016)CrossRefGoogle Scholar
  57. 57.
    C.H. Hommes, J. Econ. Dyn. Control 35, 1 (2011)MathSciNetCrossRefGoogle Scholar
  58. 58.
    C.H. Hommes, Behavioural Rationality and Heterogeneous Expectations in Complex Economic Systems (Cambridge University Press, Cambridge, UK, 2013)Google Scholar
  59. 59.
    C.H. Hommes, T. Lux, Macroeconomic Dynamics 18, 373 (2013)CrossRefGoogle Scholar
  60. 60.
    C.H. Hommes, F. Wagener, Complex Evolutionary Systems in Behavioral Finance, in Thorsten Hens and Klaus Reiner Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution (North-Holland, 2009), pp. 217–276Google Scholar
  61. 61.
    B.I. Jacobs, K.N. Levy, H.M. Markowitz, Fin. Analyst. J. 66, 42 (2010)CrossRefGoogle Scholar
  62. 62.
    B. Kelly, H. Jiang, Rev. Fin. Studies 27, 2841 (2014)CrossRefGoogle Scholar
  63. 63.
    J.L. Kelly, Bell Syst. Tech. J. 35, 917 (1956)CrossRefGoogle Scholar
  64. 64.
    A.E. Khandani, A.W. Lo, R.C. Merton, J. Fin. Econ. 108, 29 (2013)CrossRefGoogle Scholar
  65. 65.
    W.B. Kinlaw, M. Kritzman, D. Turkington, The Divergence of High and Low-frequency Estimation: Implications for Performance Measurement, Technical report, State Street Global Exchange, 2014Google Scholar
  66. 66.
    K. Kollman, J. Miller, S.E. Page, Am. Econ. Rev. 87, 977 (1997)Google Scholar
  67. 67.
    A.S. Kyle, A.A. Obizhaeva, Market Microstructure Invariants: Empirical Hypothesis, Technical Report, University of Maryland, 2016Google Scholar
  68. 68.
    D. Ladley, KR. Schenk-Hoppe, J. Econ. Dyn. Control 33, 817 (2009)CrossRefGoogle Scholar
  69. 69.
    B. LeBaron, Quant. Finance 1, 621 (2001)MathSciNetCrossRefGoogle Scholar
  70. 70.
    B. LeBaron, Agent-based Financial Markets: Matching Stylized Facts With Style, in D. Colander, editor, Post Walrasian Macroeconomics (Cambridge University Press, 2006), pp. 221–235Google Scholar
  71. 71.
    B. LeBaron, East. Econ. J. 37, 35 (2011)CrossRefGoogle Scholar
  72. 72.
    B. LeBaron, J. Econ. Behav. Organ. 83, 424 (2012)CrossRefGoogle Scholar
  73. 73.
    B. LeBaron, Heterogeneous Agents and Long Horizon Features of Asset Prices, Technical report, Brandeis International Business School, 2013Google Scholar
  74. 74.
    M. Leiss, H.H. Nax, D. Sornette, J. Econ. Dyn. Control 55, 1 (2015)CrossRefGoogle Scholar
  75. 75.
    R.E. LucasJr., Carnegie-Rochester Conference Series on Public Policy 1, 19 (1976)CrossRefGoogle Scholar
  76. 76.
    T. Lux, M. Marchesi, Nature 397, 493 (1999)ADSCrossRefGoogle Scholar
  77. 77.
    T. Lux, Stochastic Behavioral Asset Pricing Models and the Stylized Facts, in Thorsten Hens and Klaus Reiner Schenk-Hoppe, editors, Handbook of Financial Markets: Dynamics and Evolution (North-Holland, 2009), pp. 161–215Google Scholar
  78. 78.
    P. Lynch, G. Zumbach, Quant. Fin. 3, 320 (2003)CrossRefGoogle Scholar
  79. 79.
    B.B. Mandelbrot, J. Business 36, 394 (1963)CrossRefGoogle Scholar
  80. 80.
    R.N. Mantegna, H.E. Stanley, Nature 376, 46 (1996)ADSCrossRefGoogle Scholar
  81. 81.
    R.N. Mantegna, Eur. Phys. J. B 11, 193 (1999)ADSCrossRefGoogle Scholar
  82. 82.
    R.C. Merton, J. Fin. Econ. 3, 125 (1976)CrossRefGoogle Scholar
  83. 83.
    A. Moreira, T. Muir, Volatility Managed Portfolios. Technical Report, Yale School of Management, 2015Google Scholar
  84. 84.
    P. Savor, M. Wilson, J. Fin. Econ. 113, 171 (2014)CrossRefGoogle Scholar
  85. 85.
    T. Schelling, Micromotives and Macrobehavior (Norton, New York, NY, 1978)Google Scholar
  86. 86.
    D. Sornette, Rep. Prog. Phys. 77, 062001 (2014)ADSCrossRefGoogle Scholar
  87. 87.
    T. Squartini, I. van Lelyveld, D. Garlaschelli, Sci. Rep. 3, 3357 (2013)ADSGoogle Scholar
  88. 88.
    N.S.P. Tay, S.C. Linn, J. Econ. Dyn. Control 25, 321 (2001)CrossRefGoogle Scholar
  89. 89.
    M. Youssefmir, B.A. Huberman, J. Econ. Behav. Organ. 32, 101 (1997)CrossRefGoogle Scholar

Copyright information

© EDP Sciences and Springer 2016

Authors and Affiliations

  1. 1.International Business School, Brandeis UniversityWalthamUSA

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