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Investigations of Financial Markets Using Statistical Physics Methods

  • Chapter
The Science of Disasters

Abstract

We begin with a brief historical note concerning the growing interest of statistical physicists in the analysis and modeling of financial markets. We then briefly discuss the key concepts of arbitrage and efficient markets. We relate these concepts to apparently ‘universal’ aspects observed in the empirical analysis of stock price dynamics in financial markets. In particular, we consider (i) the empirical behavior of the probability density function for the return of an economic time series to where it started and (ii) the content of economic information in a financial time series.

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References

  1. L. Bachelier, Ann. Sci. l’Eeole Norm. Super. III-17, 21 (1900).

    MathSciNet  Google Scholar 

  2. P.H. Cootner (ed.), The Random Character of Stock Market Prices (MIT, Cambridge, 1964).

    Google Scholar 

  3. J.E. Ingersoll Jr., Theory of Financial Decision Making (Rowman and Littlefield, Savage, 1987).

    Google Scholar 

  4. R.C. Merton, Continuous-Time Finance (Blackwell, Cambridge, 1990).

    Google Scholar 

  5. I. Karatzas and S.E. Shreve, Brownian Motion and Stochastic Calculus, 2nd edn. (Springer, Berlin, 1991).

    Book  MATH  Google Scholar 

  6. J.Y. Campbell, A.W. Lo, and A.C. MacKinlay, The Econometrics of Financial Markets, (Princeton University Press, Princeton, 1997).

    MATH  Google Scholar 

  7. R.N. Mantegna (ed.), Proceedings of the International Workshop on Econophysics and Statistical Finance, Physica A [special issue] 269 (1999).

    Google Scholar 

  8. J.-P. Bouchaud, K. Lauritsen, and P. Alstrom (eds.), Proceedings of the International Conference on Applications in Finacial Analysis, Int. J. Theor. Appl. Finance [special issue] 3(3), 309 (2000).

    Google Scholar 

  9. J.-P. Bouchaud and M. Potters, Theory of Financial Risk (Cambridge University Press, Cambridge, 2000).

    Google Scholar 

  10. R.N. Mantegna and H.E. Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge University Press, Cambridge, 2000).

    Google Scholar 

  11. G. Parisi, Physica A 263, 557 (1999).

    Article  MathSciNet  ADS  Google Scholar 

  12. F. Black and M. Scholes, J. Polit. Econ. 81, 637 (1973).

    Article  Google Scholar 

  13. R.N. Mantegna, Physica A 179, 232 (1991).

    Article  ADS  Google Scholar 

  14. R.N. Mantegna and H.E. Stanley, Nature 376, 46 (1995).

    Article  ADS  Google Scholar 

  15. S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner, and Y. Dodge, Nature 381, 767 (1996).

    Article  ADS  Google Scholar 

  16. M. Potters, R. Cont, and J.-P. Bouchaud, Europhys. Lett. 41, 239 (1998).

    Article  ADS  Google Scholar 

  17. P. Gopikrishnan, M. Meyer, L.A.N. Amaral, and H.E. Stanley, Eur. Phys. J. B 3, 139 (1998).

    Article  ADS  Google Scholar 

  18. W. Li, Int. J. Bifurcat. Chaos 1, 583 (1991).

    MATH  Google Scholar 

  19. R.N. Mantegna and H.E. Stanley, Nature 383, 587 (1996).

    Article  ADS  Google Scholar 

  20. Y. Liu, P. Cizeau, M. Meyer, C.-K. Peng, and H.E. Stanley, Physica A 245, 437 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  21. R. Cont, M. Potters, and J.-P. Bouchaud, in Scale Invariance and Beyond, edited by B. Dubrulle, F. Graner and D. Sornette (Springer, Berlin, 1997).

    Google Scholar 

  22. A. Arneodo, J.F. Muzy, and D. Sornette, Eur. Phys. J. B 2, 277 (1998).

    Article  ADS  Google Scholar 

  23. U. A. Müller, M.M. Dacorogna, R.B. Olsen, O.V. Bietet, M. Schwarz, and G. Morgenegg, J. Banking Finance 14, 1189 (1995).

    Article  Google Scholar 

  24. P. Cizeau, Y. Liu, M. Meyer, C.-K. Peng, and H.E. Stanley, Physica A 245, 441 (1997).

    Article  MathSciNet  ADS  Google Scholar 

  25. J.-P. Bouchaud and R. Cont, Eur. Phys. J. B 6, 543 (1998).

    Article  ADS  Google Scholar 

  26. H. Takayasu, H. Miura, T. Hirabayashi, and K. Hamada, Physica A 184, 127 (1992).

    Article  ADS  Google Scholar 

  27. P. Bak, K. Chen, J. Scheinkman, and M. Woodford, Ric. Econ. 47, 3 (1993).

    Article  MATH  Google Scholar 

  28. D. Challet and Y.-C. Zhang, Physica A 256, 514 (1998).

    Article  Google Scholar 

  29. M. Levy and S. Solomon, Int. J. Mod. Phys. G 7, 595 (1996).

    Article  ADS  Google Scholar 

  30. G. Caldarein, M. Marsih, and Y.-C. Zhang, Europhys. Lett. 40, 479 (1997).

    Article  ADS  Google Scholar 

  31. M. Lévy, H. Lévy, and S. Solomon, J. Phys. I France 5, 1087 (1995).

    Article  Google Scholar 

  32. B.B. Mandelbrot, Fractals and Scaling in Finance (Springer, New York, 1997).

    MATH  Google Scholar 

  33. S. Maslov and Y.-C. Zhang, Physica 262, 232 (1999).

    Article  MathSciNet  Google Scholar 

  34. P. Bak, M. Paczuski, and M. Shubik, Physica A 246, 430 (1997).

    Article  ADS  Google Scholar 

  35. A.H. Sato and H. Takayasu, Physica A 250, 231 (1998).

    Article  MATH  Google Scholar 

  36. D. Sornette and A. Johansen, Physica A 261, 581 (1998).

    Article  MathSciNet  Google Scholar 

  37. D. Stauffer, Ann. Phys.-Berlin 7, 529 (1998).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  38. D. Stauffer and T.J.P. Penna, Physica A 256, 284 (1998).

    Article  Google Scholar 

  39. H. Takayasu, A.H. Sato, and M. Takayasu, Phys. Rev. Lett. 79, 966 (1997).

    Article  ADS  MATH  Google Scholar 

  40. T. Lux, J. Econ. Dyn. Control 22, 1 (1997).

    Article  MATH  Google Scholar 

  41. T. Lux, J. Econ. Behav. Organ. 33, 143 (1998).

    Article  Google Scholar 

  42. T. Lux and M. Marchesi, Nature 397, 498 (1999).

    Article  ADS  Google Scholar 

  43. J.-P. Bouchaud and D. Sornette, J. Phys. I France 4, 863 (1994).

    Article  MATH  Google Scholar 

  44. E. Aurell and S.L Simdyankin, Int. J. Theor. Appl. Finance 1, 1 (1998).

    Article  MATH  Google Scholar 

  45. R. Baviera, M. Pasquini, M. Serva, and A. Vulpiani, Int. J. Theor. Appl. Finance 1, 473 (1998).

    Article  MATH  Google Scholar 

  46. S. Galluccio and Y.-C. Zhang, Phys. Rev. E 54, R4516 (1996).

    Article  ADS  Google Scholar 

  47. S. Galluccio, J.-P. Bouchaud, and M. Potters, Physica A 259, 449 (1998).

    Article  Google Scholar 

  48. M. Marsih, S. Maslov, and Y.-C. Zhang, Physica A 253, 403 (1998).

    Article  Google Scholar 

  49. D. Sornette, Physica A 256, 251 (1998).

    Article  MathSciNet  Google Scholar 

  50. R.N. Mantegna and H.E. Stanley, Physica A 239, 255 (1997).

    Article  ADS  Google Scholar 

  51. J.D. Farmer, Market force, ecology, and evolution; [available from http://xxx.lanl.gov/abs/adap-org/9812005].

  52. N. Vandewalle and M. Ausloos, Physica A 246, 454 (1997).

    Article  ADS  Google Scholar 

  53. M.H.R. Stanley, L.A.N. Amaral, S.V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M.A. Salinger, and H.E. Stanley, Nature 379, 804 (1996).

    Article  ADS  Google Scholar 

  54. L.A.N. Amaral, S.V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M.A. Salinger, H.E. Stanley, and M.H.R. Stanley, J. Phys. I France 7, 621 (1997).

    Article  Google Scholar 

  55. L.A.N. Amaral, S.V. Buldyrev, S. Havlin, M.A. Salinger, and H.E. Stanley, Phys. Rev. Lett. 80, 1385 (1998).

    Article  ADS  Google Scholar 

  56. H. Takayasu and K. Okuyama, Fractals 6, 67 (1998).

    Article  Google Scholar 

  57. Y. Lee, L.A.N. Amaral, D. Canning, M. Meyer, and H.E. Stanley, Phys. Rev. Lett. 81, 3275 (1998).

    Article  ADS  Google Scholar 

  58. E. Majorana, Scientia 36, 58 (1942).

    Google Scholar 

  59. L.P. Kadanoff, Simulation 16, 261 (1971).

    Article  Google Scholar 

  60. E.W. Montroll and W.W. Badger, Introduction to Quantitative Aspects of Social Phenomena (Gordon and Breach, New York, 1974).

    Google Scholar 

  61. P.W. Anderson, J.K. Arrow, and D. Pines (eds.). The Economy as an Evolving Complex System (Addison-Wesley, Redwood City, 1988).

    MATH  Google Scholar 

  62. V. Pareto, Cours d’Economie Politique, (F. Rouge, Lausanne and Paris, 1897).

    Google Scholar 

  63. P. Levy, Calcul des Probabilités (Gauthier-Villars, Paris, 1925).

    MATH  Google Scholar 

  64. B.B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, 1982).

    MATH  Google Scholar 

  65. H.E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1971).

    Google Scholar 

  66. A. Einstein, Ann. Phys. 17, 549 (1905).

    Article  MATH  Google Scholar 

  67. N. Wiener, J. Math. Phys. 2, 131 (1923).

    Google Scholar 

  68. B.B. Mandelbrot, J. Bus. 36, 394 (1963).

    Article  Google Scholar 

  69. B.V. Gnedenko and A.N. Kolmogorov, Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, Cambridge, 1954).

    MATH  Google Scholar 

  70. E.F. Fama, J. Finance 25, 383 (1970).

    Article  Google Scholar 

  71. P.A. Samuelson, Industrial Management Rev. 6, 41 (1965).

    Google Scholar 

  72. J.L. Doob, Stochastic Processes (Wiley, New York, 1953).

    MATH  Google Scholar 

  73. E.F. Fama, J. Finance 46, 1575 (1991).

    Article  Google Scholar 

  74. J.C. Hull, Options, Futures, and Other Derivatives, 3rd edn. (Prentice-Hall, Upper Saddle River, 1997).

    Google Scholar 

  75. D. Duffie and J. Pan, J. Deriv. [spring issue], 7 (1997).

    Google Scholar 

  76. Y. Liu, P. Gopikrishnan, P. Cizeau, M. Meyer, C.-K. Peng, and H.E. Stanley, Phys. Rev. E 60, 1390 (1999).

    Article  ADS  Google Scholar 

  77. Z. Palagyi and R N. Mantegna, Physica A 269, 132 (1999).

    Article  ADS  Google Scholar 

  78. R. Baviera, M. Pasquini, M. Serva, D. Vergni, and A. Vulpiani, Efficiency in foreign exchange markets (1999); [available from http://xxx.lanl.gov/abs/cond-niat/9901225].

    Google Scholar 

  79. M.M. Dacorogna, U.A. Müller, R.J. Nagler, R.B. Olsen, and O.V. Bietet, J. Int. Money Finance 12, 413 (1993).

    Article  Google Scholar 

  80. M. Pasquini and M. Serva, Physica A 269, 140 (1999).

    Article  ADS  Google Scholar 

  81. M. Raberto, E. Scalas, G. Cuniberti, and M. Riani, Physica A 269, 148 (1999).

    Article  ADS  Google Scholar 

  82. R.F. Engle, Econometrica 50, 987 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  83. T. Bollerslev, J. Economet. 31, 307 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  84. P.K. Clark, Econometrica 41, 135 (1973).

    Article  MathSciNet  MATH  Google Scholar 

  85. R.C. Merton, J. Financ. Econ. 3, 125 (1976).

    Article  MATH  Google Scholar 

  86. R.N. Mantegna and H.E. Stanley, Phys. Rev. Lett. 73, 2946 (1994).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  87. T. Lux, Appl. Financ. Econ. 6, 463 (1996).

    Google Scholar 

  88. A.L. Tucker, J. Bus. Econ. Statist. 10, 73 (1992).

    Google Scholar 

  89. P. Gopikrishnan, V. Plerou, L.A.N. Amaral, M. Meyer, and H.E. Stanley, Phys. Rev. E 60, 5305 (1999).

    Article  ADS  Google Scholar 

  90. V. Plerou, P. Gopikrishnan, L.A.N. Amaral, M. Meyer, and H.E. Stanley, Phys. Rev. E 60, 6519 (1999).

    Article  ADS  Google Scholar 

  91. H. Markowitz, Portfolio Selection: Efficient Diversification of Investment (Wiley, New York, 1959).

    Google Scholar 

  92. R.N. Mantegna, Eur. Phys. J. B 11, 193 (1999).

    Article  ADS  Google Scholar 

  93. L. Laloux, P. Cizeau, J.-P. Bouchaud, and M. Potters, Phys. Rev. Lett. 83, 1468 (1999).

    Article  ADS  Google Scholar 

  94. V. Plerou, P. Gopikrishnan, B. Rosenow, L.A.N. Amaral, and H.E. Stanley, Phys. Rev. Lett. 83, 1471 (1999).

    Article  ADS  Google Scholar 

  95. A.M. Sengupta and P.P. Mitra, Phys. Rev. E 60, 3389 (1999).

    Article  ADS  Google Scholar 

  96. P. Gopikrishnan, B. Rosenow, V. Plerou, and H.E. Stanley, Phys. Rev. E. Rapid Communications 64, 035106-1 (2001).

    Google Scholar 

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Authors
  1. Rosario N. Mantegna
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  2. H. Eugene Stanley
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© 2002 Springer-Verlag Berlin Heidelberg

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Mantegna, R.N., Stanley, H.E. (2002). Investigations of Financial Markets Using Statistical Physics Methods. In: The Science of Disasters. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56257-0_12

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  • DOI: https://doi.org/10.1007/978-3-642-56257-0_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-62531-2

  • Online ISBN: 978-3-642-56257-0

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