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

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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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    References listed on IDEAS

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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.

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    More about this item

    Keywords

    Stylized Facts; Student Processes; Hyperbolic Distributions; Renormalization Group;
    All these keywords.

    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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