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Distributions of historic market data – stock returns

  • Zhiyuan Liu
  • M. Dashti Moghaddam
  • R. A. SerotaEmail author
Regular Article
  • 3 Downloads

Abstract

We show that the moments of the distribution of historic stock returns are in excellent agreement with the Heston model and not with the multiplicative model, which predicts power-law tails of volatility and stock returns. We also show that the mean realized variance of returns is a linear function of the number of days over which the returns are calculated. The slope is determined by the mean value of the variance (squared volatility) in the mean-reverting stochastic volatility models, such as Heston and multiplicative, independent of stochasticity. The distribution function of stock returns, which rescales with the increase of the number of days of return, is obtained from the steady-state variance distribution function using the product distribution with the normal distribution.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

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Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Zhiyuan Liu
    • 1
  • M. Dashti Moghaddam
    • 1
  • R. A. Serota
    • 1
    Email author
  1. 1.Department of PhysicsUniversity of CincinnatiCincinnatiUSA

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