Distributions of historic market data – stock returns

Zhiyuan Liu, M. Dashti Moghaddam and R. A. Serota ()
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Zhiyuan Liu: University of Cincinnati
M. Dashti Moghaddam: University of Cincinnati
R. A. Serota: University of Cincinnati

The European Physical Journal B: Condensed Matter and Complex Systems, 2019, vol. 92, issue 3, 1-10

Abstract: 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 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (2)

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DOI: 10.1140/epjb/e2019-90218-8

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