Turbulent cascades in foreign exchange markets (2024)

Table of Contents
Abstract Access options Additional access options: References Author information Authors and Affiliations Rights and permissions About this article Cite this article This article is cited by Universal equation of state for wave turbulence in a quantum gas The prevalence of chaotic dynamics in games with many players Multiplicative random cascades with additional stochastic process in financial markets Turbulence hierarchy in a random fibre laser Emergence of a turbulent cascade in a quantum gas Comments
  • Letter
  • Published: 27 June 1996
  • S. Ghashghaie1,
  • W. Breymann2,
  • J. Peinke3,
  • P. Talkner4 &
  • …
  • Y. Dodge5

Nature volume381,pages 767–770 (1996)Cite this article

  • 1228 Accesses

  • 498 Citations

  • 20 Altmetric

  • Metrics details

Abstract

THE availability of high-frequency data for financial markets has made it possible to study market dynamics on timescales of less than a day1. For foreign exchange (FX) rates Müller et al.2 have shown that there is a net flow of information from long to short timescales: the behaviour of long-term traders (who watch the markets only from time to time) influences the behaviour of short-term traders (who watch the markets continuously). Motivated by this hierarchical feature, we have studied FX market dynamics in more detail, and report here an analogy between these dynamics and hydrodynamic turbulence3–8. Specifically, the relationship between the probability density of FX price changes (δx) and the time delay (δt) (Fig. la) is much the same as the relationship between the probability density of the velocity differences (δv) of two points in a turbulent flow and their spatial separation δr (Fig. 1b). Guided by this similarity we claim that there is an information cascade in FX market dynamics that corresponds to the energy cascade in hydrodynamic turbulence. On the basis of this analogy we can now rationalize the statistics of FX price differences at different time delays, which is important for, for example, option pricing. The analogy also provides a conceptual framework for understanding the short-term dynamics of speculative markets.

This is a preview of subscription content, access via your institution

Access options

Access through your institution

Change institution

Buy or subscribe

Subscribe to this journal

Receive 51 print issues and online access

$199.00 per year

only $3.90 per issue

Learn more

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

References

  1. Proc. lst Int. Conf. on High Frequency Data in Finance (Olsen & Associates, Zürich, 1995).

  2. Müller, U. A. et al. J. empirical Fin. (in the press).

  3. Landau, L. D. & Lifsh*tz, E. M. Fluid Mechanics 2nd edn (Pergamon, Oxford, 1987).

    Google Scholar

  4. Monin, A. S. & Yaglom, A. M. Statistical Fluid Mechanics Vols 1 & 2 (ed. Lumely, J.) (MIT Press, Cambridge, MA, 1971 & 1975).

    Google Scholar

  5. Kolmogorov, A. N. J. Fluid Mech. 13, 82–85 (1962).

    Article ADS MathSciNet Google Scholar

  6. Obukhov, A. M. J. Fluid Mech. 13, 77–81 (1962).

    Article ADS MathSciNet Google Scholar

  7. Castaing, B., Gagne, Y. & Hopfinger, E. Physica D46, 177–200 (1990).

    Google Scholar

  8. Kolmogorov, A. N. Dokl. Akad. Nauk. SSSR 30, 301–305 (1941).

    ADS Google Scholar

  9. Müller, U. A. et al. J. Banking Fin. 14, 1189–1208 (1990).

    Article Google Scholar

  10. Mantegna, R. N. & Stanley, H. E. Nature 376, 46–49 (1995).

    Article ADS CAS Google Scholar

  11. Baillie, R. T. & Bollerslev, T. J. Business econ. Statist. 7, 297–305 (1989); Rev. econ. Stud. 58, 565–585 (1991).

    Google Scholar

  12. Vassilicos, J. C. Nature 374, 408–409 (1995).

    Article ADS CAS Google Scholar

  13. Chabaud, B. et al. Phys. Rev. Lett. 73, 3227–3230 (1994).

    Article ADS CAS Google Scholar

  14. Peinke, J. et al. in Fractals in the Natural and Applied Sciences Vol. A41, (ed. Novak, M. M.) 295–304 (Elsevier Science Amsterdam, 1994).

    Google Scholar

  15. Naert, A. et al. J. Phys. II Fr. 4, 215–224 (1994).

    Google Scholar

  16. Granger, C. W. & Orr, D. J. J. Am. statist. Ass. 67, 275–285 (1972).

    Google Scholar

  17. Clark, P. K. Econometrica 41, 135–155 (1973).

    Article MathSciNet Google Scholar

  18. Kon, S. J. J. Fin. 39, 147–165 (1984).

    Google Scholar

  19. Engle, R. F. Econometrica 50, 987–1007 (1982).

    Article MathSciNet Google Scholar

  20. Bollerslev, T., Chous, R. Y. & Kroner, K. F. J. Econometrics 52, 5–59 (1992).

    Article Google Scholar

  21. Taylor, S. J. Math. Fin. 4, 183–204 (1994).

    Article Google Scholar

  22. Stolovitzky, G., Sreenivasan, K. R. & Juneja, A. Phys. Rev. E48, 3217–3220 (1993).

    ADS Google Scholar

  23. Anselmet, F., Gagne, Y., Hopfinger, E. J. & Antonia, R. A. J. Fluid Mech. 140, 63–89 (1984).

    Article ADS Google Scholar

  24. Richardson, L. F. Weather Prediction by Numerical Process 66 (Cambridge Univ. Press, 1922).

    MATH Google Scholar

Download references

Author information

Authors and Affiliations

  1. Fürstensteinerstrasse 4, 4053, Basel, Switzerland

    S. Ghashghaie

  2. Institute für Physik der Universität Basel, 4056, Basel, Switzerland

    W. Breymann

  3. Experimentalphysik II, Universität Bayreuth, 95440, Bayreuth, Germany

    J. Peinke

  4. Paul Scherrer Institut, 5232, Villigen, Switzerland

    P. Talkner

  5. Groupe de Statistiques, Université de Neuchâtel, 2000, Neuchâtel, Switzerland

    Y. Dodge

Authors

  1. S. Ghashghaie

    View author publications

    You can also search for this author in PubMedGoogle Scholar

  2. W. Breymann

    View author publications

    You can also search for this author in PubMedGoogle Scholar

  3. J. Peinke

    View author publications

    You can also search for this author in PubMedGoogle Scholar

  4. P. Talkner

    View author publications

    You can also search for this author in PubMedGoogle Scholar

  5. Y. Dodge

    View author publications

    You can also search for this author in PubMedGoogle Scholar

Rights and permissions

About this article

Cite this article

Ghashghaie, S., Breymann, W., Peinke, J. et al. Turbulent cascades in foreign exchange markets. Nature 381, 767–770 (1996). https://doi.org/10.1038/381767a0

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/381767a0

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Turbulent cascades in foreign exchange markets (2024)
Top Articles
Wedding Cakes From Walmart | LoveToKnow
Is My Baked Potato Safe to Eat?
4-3 Assignment Identifying Your Thesis Statement
In the Dark of Winter, We Can See His Light - Jesus Calling
Bruce Mair FREC on LinkedIn: "Is it worth applying for a vacancy which has had 100+ applicants already?…
Who is Keir Starmer, the self-described socialist set to lead the U.K.? Some Brits still don't know
Guitar Center Trade in Values: Is it Worth it in 2023? - Guitar Lobby
Gitaar kopen bij MUSIC STORE - Nederlands | MUSIC STORE professional
Go Upstate Mugshots Gaffney Sc
Steam Grid Db Manager
Melvor Dungeon Guide
Thousands of North Carolinians now eligible for COVID-19 booster
Latest Posts
This Is How Long Your Pasta Sauce Lasts in the Refrigerator
Chili With Corn - Easy Budget Recipes
Article information

Author: Nathanial Hackett

Last Updated:

Views: 6706

Rating: 4.1 / 5 (72 voted)

Reviews: 87% of readers found this page helpful

Author information

Name: Nathanial Hackett

Birthday: 1997-10-09

Address: Apt. 935 264 Abshire Canyon, South Nerissachester, NM 01800

Phone: +9752624861224

Job: Forward Technology Assistant

Hobby: Listening to music, Shopping, Vacation, Baton twirling, Flower arranging, Blacksmithing, Do it yourself

Introduction: My name is Nathanial Hackett, I am a lovely, curious, smiling, lively, thoughtful, courageous, lively person who loves writing and wants to share my knowledge and understanding with you.