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Exponential distribution of financial returns at mesoscopic time lags: a new stylized fact

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  • A. Christian Silva
  • Richard E. Prange
  • Victor M. Yakovenko
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    Abstract

    We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times the bulk of the distribution (more than 99% of the probability) follows an exponential law. The slope of the exponential function is determined by the variance of returns, which increases proportionally to the time lag. At longer times, the exponential law continuously evolves into Gaussian distribution. The exponential-to-Gaussian crossover is well described by the analytical solution of the Heston model with stochastic volatility.

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    File URL: http://arxiv.org/pdf/cond-mat/0401225
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0401225.

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    Date of creation: Jan 2004
    Date of revision: Jul 2004
    Publication status: Published in Physica A 344, 227-235 (2004)
    Handle: RePEc:arx:papers:cond-mat/0401225

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    Web page: http://arxiv.org/

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