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Stochastic volatility of financial markets as the fluctuating rate of trading: An empirical study

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  • Silva, A. Christian
  • Yakovenko, Victor M.

Abstract

We present an empirical study of the subordination hypothesis for a stochastic time series of a stock price. The fluctuating rate of trading is identified with the stochastic variance of the stock price, as in the continuous-time random walk (CTRW) framework. The probability distribution of the stock price changes (log-returns) for a given number of trades N is found to be approximately Gaussian. The probability distribution of N for a given time interval Δt is non-Poissonian and has an exponential tail for large N and a sharp cutoff for small N. Combining these two distributions produces a non-trivial distribution of log-returns for a given time interval Δt, which has exponential tails and a Gaussian central part, in agreement with empirical observations.

Suggested Citation

  • Silva, A. Christian & Yakovenko, Victor M., 2007. "Stochastic volatility of financial markets as the fluctuating rate of trading: An empirical study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 278-285.
    • Handle: RePEc:eee:phsmap:v:382:y:2007:i:1:p:278-285
    DOI: 10.1016/j.physa.2007.03.051
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    Cited by:

    1. Alessio Emanuele Biondo, 2018. "Order book microstructure and policies for financial stability," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 35(1), pages 196-218, March.
    2. Seemann, Lars & McCauley, Joseph L. & Gunaratne, Gemunu H., 2011. "Intraday volatility and scaling in high frequency foreign exchange markets," International Review of Financial Analysis, Elsevier, vol. 20(3), pages 121-126, June.
    3. Biondo, Alessio Emanuele, 2017. "Learning to forecast, risk aversion, and microstructural aspects of financial stability," Economics Discussion Papers 2017-104, Kiel Institute for the World Economy (IfW Kiel).
    4. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
    5. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    6. de Mattos Neto, Paulo S.G. & Silva, David A. & Ferreira, Tiago A.E. & Cavalcanti, George D.C., 2011. "Market volatility modeling for short time window," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3444-3453.
    7. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    8. Romanovsky, M.Yu. & Vidov, P.V., 2011. "Analytical representation of stock and stock-indexes returns: Non-Gaussian random walks with various jump laws," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3794-3805.
    9. Hua, Jia-Chen & Chen, Lijian & Falcon, Liberty & McCauley, Joseph L. & Gunaratne, Gemunu H., 2015. "Variable diffusion in stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 221-233.
    10. A. Christian Silva & Ju-Yi Yen, 2010. "Stochastic resonance and the trade arrival rate of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 10(5), pages 461-466.
    11. Dashti Moghaddam, M. & Serota, R.A., 2021. "Combined multiplicative–Heston model for stochastic volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    12. James Primbs & Muruhan Rathinam, 2009. "Trader Behavior and its Effect on Asset Price Dynamics," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(2), pages 151-181.
    13. Ata Türkoğlu, 2016. "Normally distributed high-frequency returns: a subordination approach," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 389-409, March.
    14. Seemann, Lars & Hua, Jia-Chen & McCauley, Joseph L. & Gunaratne, Gemunu H., 2012. "Ensemble vs. time averages in financial time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6024-6032.
    15. Wei, Yu, 2012. "Forecasting volatility of fuel oil futures in China: GARCH-type, SV or realized volatility models?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5546-5556.

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