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The ups and downs of the renormalization group applied to financial time series

Author

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  • Challet, Damien
  • Peirano, Pier Paolo

Abstract

Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently devised a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Levy distributions; we also show that the analytic tractability of the model extends to the larger class of symmetric generalized hyperbolic distributions and provide a full computation of their multivariate characteristic functions. The Baldovin and Stella model, while mimicking well volatility relaxation phenomena such as the Omori law, fails to reproduce other stylized facts such as the leverage effect or some time reversal asymmetries. We discuss how to modify the dynamics of this process in order to reproduce real data more accurately.

Suggested Citation

  • Challet, Damien & Peirano, Pier Paolo, 2008. "The ups and downs of the renormalization group applied to financial time series," MPRA Paper 9770, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:9770
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    File URL: https://mpra.ub.uni-muenchen.de/16358/2/MPRA_paper_16358.pdf
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    References listed on IDEAS

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    1. Drożdż, S. & Forczek, M. & Kwapień, J. & Oświe¸cimka, P. & Rak, R., 2007. "Stock market return distributions: From past to present," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 59-64.
    2. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    3. Bacry, Emmanuel & Kozhemyak, Alexey & Muzy, Jean-François, 2006. "Are asset return tail estimations related to volatility long-range correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 119-126.
    4. Lisa Borland, 2002. "Option Pricing Formulas based on a non-Gaussian Stock Price Model," Papers cond-mat/0204331, arXiv.org, revised Sep 2002.
    5. Benoit Mandelbrot & Adlai Fisher & Laurent Calvet, 1997. "A Multifractal Model of Asset Returns," Cowles Foundation Discussion Papers 1164, Cowles Foundation for Research in Economics, Yale University.
    6. Gilles Zumbach, 2004. "Volatility processes and volatility forecast with long memory," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 70-86.
    7. Jean-Philippe Bouchaud & Marc Potters & Martin Meyer, 1999. "Apparent multifractality in financial time series," Science & Finance (CFM) working paper archive 9906347, Science & Finance, Capital Fund Management.
    8. Dreier, I. & Kotz, S., 2002. "A note on the characteristic function of the t-distribution," Statistics & Probability Letters, Elsevier, vol. 57(3), pages 221-224, April.
    9. S. Drozdz & M. Forczek & J. Kwapien & P. Oswiecimka & R. Rak, 2007. "Stock market return distributions: from past to present," Papers 0704.0664, arXiv.org.
    10. Paul Lynch & Gilles Zumbach, 2003. "Market heterogeneities and the causal structure of volatility," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 320-331.
    11. F. Lillo, 2007. "Limit order placement as an utility maximization problem and the origin of power law distribution of limit order prices," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(4), pages 453-459, February.
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    Cited by:

    1. Fulvio Baldovin & Francesco Camana & Michele Caraglio & Attilio L. Stella & Marco Zamparo, 2012. "Aftershock prediction for high-frequency financial markets' dynamics," Papers 1203.5893, arXiv.org, revised Jul 2012.

    More about this item

    Keywords

    Stylized Facts; Student Processes; Hyperbolic Distributions; Renormalization Group;

    JEL classification:

    • C40 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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