Market price simulator based on analog electrical circuit

  • Aki-Hiro Sato
  • Hideki Takayasu
Conference paper


We constructed an analog electrical circuit which generates fluctuations in which probability density function has power law tails. In the circuit fluctuations with an arbitrary exponent of the power law can be obtained by adjusting the resistance. With this low cost circuit the random fluctuations which have the similar statistics to foreign exchange rates can be generated as fast as an expensive digital computer.

Key words

random multiplicative process power law foreign currency rate analog electrical circuit 


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  1. 1.
    Bak P., Paczzuski M. and Shubik M. (1997) Price variations in a stock market with many agents. Physica A 246:430–453.ADSCrossRefGoogle Scholar
  2. 2.
    Deutsch J.M. (1994) Probability distributions for one component equations with multiplicative noise. Physica A 208:433–444.ADSCrossRefGoogle Scholar
  3. 3.
    Jögi P., Sornette D. and Blank M. (1998) Fine structure and complex exponents in power-law distribution from random maps. Phys. Rev. E 57:120–134.CrossRefGoogle Scholar
  4. 4.
    Kuramoto Y. and Nakao H. (1996) Origin of power-law spatial correlations in distributed oscillators and maps with nonlinear coupling. Phys. Rev. Lett. 76:4352–4355.ADSCrossRefGoogle Scholar
  5. 5.
    Lux T. and Marchesi M. (1999) Scaling and criticality in a stochastic multiagnet model of a financial market. Nature (London) 397:498–500.ADSCrossRefGoogle Scholar
  6. 6.
    Mantegna R.N. and Stanley H.E. (1995) Scaling behavior in the dynamics of an economics index. Nature (London) 376:46–49.ADSCrossRefGoogle Scholar
  7. 7.
    Nakao H. (1998) Asymptotic power law of moments in a random multiplicative process with weak additive noise. Phy. Rev. E 58:1591–1601.MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Sato A.-H. and Takayasu H. (1998) Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness. Physica A 250:231–252.zbMATHCrossRefGoogle Scholar
  9. 9.
    Sato A.-H., Takayasu H. and Sawada Y. (2000) Invariant power law distribution of Langevin systems with colored multiplicative noise. Phys. Rev. E 61:1081–1087.ADSCrossRefGoogle Scholar
  10. 10.
    Sato A.-H., Takayasu H. and Sawada Y. (2000) Power law fluctuation generator based on analog electrical circuit. Fractals 8:219–225.Google Scholar
  11. 11.
    Takayasu H., Sato A.-H. and Takayasu M. (1997) Stable infinite variance fluctuations in randomly amplified Langevin systems. Phys. Rev. Lett. 79:966–969.ADSzbMATHCrossRefGoogle Scholar
  12. 12.
    Takayasu H. and Takayasu M. (1999) Critical fluctuations of demand and supply. Physica A 269:24–29.ADSCrossRefGoogle Scholar
  13. 13.
    Takayasu H., Takayasu M., Okazaki M.P., Marumo K. and Shimizu T. (2000) Fractal properties in economics.In:Novak M.(Ed.) Paradigms of Complexity, World Scientific, 243–257.Google Scholar
  14. 14.
    Venkataramani S.C., Antonsen Jr. T.M., Ott E. and Sommerer J.C. (1996) Onoff intermittency: Power spectrum and fractal properties of time series. Physica D 96:66–99.MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • Aki-Hiro Sato
    • 1
  • Hideki Takayasu
    • 2
  1. 1.Department of Applied Mathematics and PhysicsKyoto UniversityKyotoJapan
  2. 2.Sony Computer Science LaboratoriesShinagawa-ku, TokyoJapan

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