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Maximum entropy distribution of stock price fluctuations

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  • Bartiromo, Rosario

Abstract

In this paper we propose to use the principle of absence of arbitrage opportunities in its entropic interpretation to obtain the distribution of stock price fluctuations by maximizing its information entropy. We show that this approach leads to a physical description of the underlying dynamics as a random walk characterized by a stochastic diffusion coefficient and constrained to a given value of the expected volatility, in this way taking into account the information provided by the existence of an option market. The model is validated by a comprehensive comparison with observed distributions of both price return and diffusion coefficient. Expected volatility is the only parameter in the model and can be obtained by analysing option prices. We give an analytic formulation of the probability density function for price returns which can be used to extract expected volatility from stock option data.

Suggested Citation

  • Bartiromo, Rosario, 2013. "Maximum entropy distribution of stock price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(7), pages 1638-1647.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:7:p:1638-1647
    DOI: 10.1016/j.physa.2012.11.048
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
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    Cited by:

    1. Gzyl, Henryk & ter Horst, Enrique & Molina, Germán, 2019. "A model-free, non-parametric method for density determination, with application to asset returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 210-221.
    2. Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    3. Claudiu Vinte & Marcel Ausloos & Titus Felix Furtuna, 2022. "A Volatility Estimator of Stock Market Indices Based on the Intrinsic Entropy Model," Papers 2205.01370, arXiv.org.

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