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Bayesian statistical inference addressed to share prices dynamics' theory

Author

Listed:
  • Geoffrey Ducournau

    (SEM, Tsinghua University; MRE, University of Montpellier; Dimtech)

  • Daniel Melhem

    (Dimtech ; MRE, University of Montpellier)

Abstract

This paper examines the Osborne' Brownian motion theory to prices dynamics. Osborne's assumption is modified to account for the asymmetry of opportunity due to agents' update of the probability of profit overtime. We provide numerical illustrations to demonstrate the underlying behavior of these dynamics by considering the change in prices under an assumed conservative system and a dissipative system. Under a conservative system, results showed that the dynamics quickly converge to a global equilibrium, which is the marginal probability of profit in a fair game. Under a dissipative system, the dynamics can be described by a superposition of distributions in local equilibrium with constant variance satisfying locally the implications of Osborne's theory. Globally, the dynamics do not reach equilibrium, and its distribution exhibits asymmetries of opportunity and is characterized by a changing variance. We finally extend our work and provide empirical evidence that the variance dynamism of the S&P500 index undergoes statistical transition from high to low timeframe. Under high frequency, the lognormal and inverted gamma distributions best explain the variance dynamism; under low frequency, the gamma distribution best explains it. This conclusion paves the way to a new approach to volatility modeling and asset pricing by considering stock returns dynamics as a superposition of statistics with known mean and unknown variance, namely a superstatistics.

Suggested Citation

  • Geoffrey Ducournau & Daniel Melhem, 2024. "Bayesian statistical inference addressed to share prices dynamics' theory," Economics Bulletin, AccessEcon, vol. 44(1), pages 373-398.
    • Handle: RePEc:ebl:ecbull:eb-21-00799
    as

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    References listed on IDEAS

    as
    1. Karl–Gustaf Lofgren & Torsten Persson & Jorgen W. Weibull, 2002. "Markets with Asymmetric Information: The Contributions of George Akerlof, Michael Spence and Joseph Stiglitz," Scandinavian Journal of Economics, Wiley Blackwell, vol. 104(2), pages 195-211, June.
    2. Mandelbrot, Benoit, 1969. "Long-Run Linearity, Locally Gaussian Process, H-Spectra and Infinite Variances," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 10(1), pages 82-111, February.
    3. Dyer, James C, IV, 1976. "Random Walks in Australian Share Prices: A Question of Efficient Capital Markets," Australian Economic Papers, Wiley Blackwell, vol. 15(27), pages 186-200, December.
    4. Eugene F. Fama, 1963. "Mandelbrot and the Stable Paretian Hypothesis," The Journal of Business, University of Chicago Press, vol. 36, pages 420-420.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Stochastic volatility; Bayesian Inference; Statistical mechanics;
    All these keywords.

    JEL classification:

    • Y1 - Miscellaneous Categories - - Data: Tables and Charts
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics

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