- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Letters

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Financial Brownian Particle in the Layered Order-Book Fluid and Fluctuation-Dissipation Relations

Yoshihiro Yura1,4, Hideki Takayasu2,3, Didier Sornette4, and Misako Takayasu1,*

  • 1Department of Computational Intelligence and Systems Science, Interdisciplinary Graduate School of Science and Engineering, Tokyo Institute of Technology 4259 Nagatsuta-cho, Yokohama 226-8502, Japan
  • 2Sony Computer Science Laboratories, 3-14-13, Higashi-Gotanda, Shinagawa-ku, Tokyo 141-0022, Japan
  • 3Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, 4-21-1 Nakano, Nakano-ku, Tokyo 164-8525, Japan
  • 4Department of Management, Technology, and Economics, ETH Zurich, Scheuchzerstrasse 7, 8092 Zurich, Switzerland

  • *takayasu@dis.titech.ac.jp
PDF

Phys. Rev. Lett. 112, 098703 – Published 7 March, 2014

DOI: https://doi.org/10.1103/PhysRevLett.112.098703

Abstract

We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian particle and its surrounding fluid particles reflect specific layering interactions; in the inner layer the correlation is strong and with short memory, while in the outer layer it is weaker and with long memory. By interpreting and estimating the contribution from the outer layer as a drag resistance, we demonstrate the validity of the fluctuation-dissipation relation in this nonmaterial Brownian motion process.

View figure in article

Article Text

References (38)

  1. L. Bachelier, Annales Scientifiques de l’École Normale Supérieure 17, 21 (1900).
  2. R. Kubo, Rep. Prog. Phys. 29, 255 (1966).
  3. H. Mori, Prog. Theor. Phys. 33, 423 (1965).
  4. F. Sciortino and P. Tartaglia, Phys. Rev. Lett. 86, 107 (2001).
  5. H. Kawamura, Phys. Rev. Lett. 90, 237201 (2003).
  6. C. Maggi, R. Di Leonardo, J. C. Dyre, and G. Ruocco, Phys. Rev. B 81, 104201 (2010).
  7. D. R. Strachan, G. C. Kalur, and S. R. Raghavan, Phys. Rev. E 73, 041509 (2006).
  8. H. Oucris and N. E. Israeloff, Nat. Phys. 6, 135 (2009).
  9. S. Joubaud, B. Percier, A. Petrosyan, and S. Ciliberto, Phys. Rev. Lett. 102, 130601 (2009).
  10. K. Komatsu, D. L’Hôte, S. Nakamae, V. Mosser, M. Konczykowski, E. Dubois, V. Dupuis, and R. Perzynski, Phys. Rev. Lett. 106, 150603 (2011).
  11. R. C. Merton, Bell Journal of economics 4, 141 (1973).
  12. A. S. Kyle, Econometrica 53, 1315 (1985).
  13. T. Hirabayashi, H. Takayasu, H. Miura, and K. Hamada, Fractals 01, 29 (1993).
  14. J. D. Farmer, Ind. Corp. Change. 11, 895 (2002).
  15. J.-P. Bouchaud and R. Cont, Eur. Phys. J. B 6, 543 (1998).
  16. K. Ide and D. Sornette, Physica (Amsterdam) 307A, 63 (2002).
  17. H. Takayasu, A.-H. Sato, and M. Takayasu, Phys. Rev. Lett. 79, 966 (1997).
  18. M. Takayasu, T. Mizuno, and H. Takayasu, Physica (Amsterdam) 370A, 91 (2006).
  19. K. Watanabe, H. Takayasu, and M. Takayasu, Phys. Rev. E 80, 056110 (2009).
  20. Y. Yura, H. Takayasu, K. Nakamura, and M. Takayasu, J. Stat. Comp. Simu. (to be published).
  21. S. V. Vikram and S. Sinha, Phys. Rev. E 83, 016101 (2011).
  22. P. Bak, M. Paczuski, and M. Shubik, Physica (Amsterdam) 246A, 430 (1997).
  23. D. L. C. Chan, D. Eliezer, and I. I. Kogan, arXiv:cond-mat/0101474.
  24. D. Challet and R. Stinchcombe, Physica (Amsterdam) 300A, 285 (2001).
  25. F. Slanina, Phys. Rev. E 64, 056136 (2001).
  26. V. Plerou, P. Gopikrishnan, and H. E. Stanley, Phys. Rev. E 71, 046131 (2005).
  27. H. Takayasu, H. Miura, T. Hirabayashi, and K. Hamada, Physica (Amsterdam) 184A, 127 (1992).
  28. K. Yamada, H. Takayasu, T. Ito, and M. Takayasu, Phys. Rev. E 79, 051120 (2009).
  29. J. Hasbrouck, Empirical Market Microstructure: The Institutions, Economics and Econometrics of Securities Trading (Oxford University Press, New York, 2007).
  30. S. Maslov, Physica (Amsterdam) 278A, 571 (2000).
  31. J.-P. Bouchaud, Y. Gefen, M. Potters, and M. Wyart, Quant. Finance 4, 176 (2004).
  32. J. D. Farmer, A. Gerig, F. Lillo, and S. Mike, Quant. Finance 6, 107 (2006).
  33. F. Lillo, J. D. Farmer, and R. N. Mantegna, Nature (London) 421, 129 (2003).
  34. P. Weber and B. Rosenow, Quant. Finance 5, 357 (2005).
  35. R. Cont, A. Kukanov, and S. Stoikov, J. Financ. Econ. 12, 47 (2013).
  36. M. Knudsen, Ann. Phys. (Leipzig) 28, 75 (1909).
  37. E. Cussler, Diffusion: Mass Transfer in Fluid Systems, Cambridge Series in Chemical Engineering (Cambridge University Press, Cambridge, England, 1997) 3rd ed.
  38. J. T. Padding and A. A. Louis, Phys. Rev. E 74, 031402 (2006).

Outline

Information

Phys. Rev. Lett. 112, 098703– Published 7 March, 2014
  • Received 12 April 2013
Creative Commons Logo

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

© 2014 Published by American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation