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A Stochastic Cascade Model For Fx Dynamics

Author

Listed:
  • WOLFGANG BREYMANN

    (Olsen & Associates, Seefeldstrasse 233, 8008 Zurich, Switzerland)

  • SHOALEH GHASHGHAIE

    (Institut für mathematische Statistik, Sidlerstr. 5, 3012 Bern, Switzerland)

  • PETER TALKNER

    (Paul Scherrer Institut, 5232 Villigen, Switzerland)

Abstract

A time series model for the FX dynamics is presented which takes into account structural peculiarities of the market, namely its heterogeneity and an information flow from long to short time horizons. The model emerges from an analogy between FX dynamics and hydrodynamic turbulence. The heterogeneity of the market is modeled in the form of a multiplicative cascade of time scales ranging from several minutes to a few months, analogous to the Kolmogorov cascade in turbulence.The model reproduces well the important empirical characteristics of FX rates for major currencies, as the heavy-tailed distribution of returns, their change in shape with the increasing time interval, and the persistence of volatility.

Suggested Citation

  • Wolfgang Breymann & Shoaleh Ghashghaie & Peter Talkner, 2000. "A Stochastic Cascade Model For Fx Dynamics," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 357-360.
    • Handle: RePEc:wsi:ijtafx:v:03:y:2000:i:03:n:s021902490000019x
    DOI: 10.1142/S021902490000019X
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    Citations

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    Cited by:

    1. Alexander Subbotin, 2008. "A multi-horizon scale for volatility," Post-Print halshs-00261514, HAL.
    2. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 9, Edward Elgar Publishing.
    3. Segnon, Mawuli & Lux, Thomas, 2013. "Multifractal models in finance: Their origin, properties, and applications," Kiel Working Papers 1860, Kiel Institute for the World Economy (IfW Kiel).
    4. Jun-ichi Maskawa & Koji Kuroda, 2020. "Model of continuous random cascade processes in financial markets," Papers 2010.12270, arXiv.org.
    5. Subbotin, Alexandre, 2009. "Volatility Models: from Conditional Heteroscedasticity to Cascades at Multiple Horizons," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 15(3), pages 94-138.
    6. Alexander Subbotin & Thierry Chauveau & Kateryna Shapovalova, 2009. "Volatility Models: from GARCH to Multi-Horizon Cascades," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00390636, HAL.
    7. Céline Azizieh & Wolfgang Breymann, 2005. "Estimation of the Stylized Facts of a Stochastic Cascade Model," Working Papers CEB 05-009.RS, ULB -- Universite Libre de Bruxelles.
    8. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW Kiel).

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