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Distributions of Historic Market Data - Stock Returns

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  • Zhiyuan Liu
  • M. Dashti Moghaddam
  • R. A. Serota

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.

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  • Zhiyuan Liu & M. Dashti Moghaddam & R. A. Serota, 2017. "Distributions of Historic Market Data - Stock Returns," Papers 1711.11003, arXiv.org, revised Dec 2017.
    • Handle: RePEc:arx:papers:1711.11003
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    References listed on IDEAS

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    6. Jaume Masoliver & Josep Perelló, 2002. "A Correlated Stochastic Volatility Model Measuring Leverage And Other Stylized Facts," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(05), pages 541-562.
    7. Praetz, Peter D, 1972. "The Distribution of Share Price Changes," The Journal of Business, University of Chicago Press, vol. 45(1), pages 49-55, January.
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    Cited by:

    1. M. Dashti Moghaddam & Zhiyuan Liu & R. A. Serota, 2019. "Distribution of Historic Market Data ¨C Implied and Realized Volatility," Applied Economics and Finance, Redfame publishing, vol. 6(5), pages 104-130, September.
    2. M. Dashti Moghaddam & R. A. Serota, 2018. "Combined Mutiplicative-Heston Model for Stochastic Volatility," Papers 1807.10793, arXiv.org.

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