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A long-range memory stochastic model of the return in financial markets

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  • V. Gontis
  • J. Ruseckas
  • A. Kononovicius
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    Abstract

    We present a nonlinear stochastic differential equation (SDE) which mimics the probability density function (PDF) of the return and the power spectrum of the absolute return in financial markets. Absolute return as a measure of market volatility is considered in the proposed model as a long-range memory stochastic variable. The SDE is obtained from the analogy with earlier proposed model of trading activity in the financial markets and generalized within the nonextensive statistical mechanics framework. The proposed stochastic model generates time series of the return with two power law statistics, i.e., the PDF and the power spectral density, reproducing the empirical data for the one minute trading return in the NYSE.

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    File URL: http://arxiv.org/pdf/0901.0903
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0901.0903.

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    Date of creation: Jan 2009
    Date of revision: Oct 2009
    Publication status: Published in Physica A 389 (2010) 100-106
    Handle: RePEc:arx:papers:0901.0903

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    Web page: http://arxiv.org/

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