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A nonextensive approach to the dynamics of financial observables

Author

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  • S. M.D. Queirós
  • L. G. Moyano
  • J. de Souza
  • C. Tsallis

Abstract

We present results about financial market observables, specifically returns and traded volumes. They are obtained within the current nonextensive statistical mechanical framework based on the entropy $S_{q}=k\frac{1-\sum_{i=1}^{W} p_{i} ^{q}}{1-q}\, (q\in \Re) \left(S_{1} \equiv S_{BG}=-k\sum_{i=1}^{W}p_{i}\,\ln p_{i}\right)$ . More precisely, we present stochastic dynamical mechanisms which mimic probability density functions empirically observed. These mechanisms provide possible interpretations for the emergence of the entropic indices q in the time evolution of the corresponding observables. In addition to this, through multi-fractal analysis of return time series, we verify that the dual relation q stat +q sens =2 is numerically satisfied, q stat and q sens being associated to the probability density function and to the sensitivity to initial conditions respectively. This type of simple relation, whose understanding remains ellusive, has been empirically verified in various other systems. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Suggested Citation

  • S. M.D. Queirós & L. G. Moyano & J. de Souza & C. Tsallis, 2007. "A nonextensive approach to the dynamics of financial observables," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 161-167, January.
    • Handle: RePEc:spr:eurphb:v:55:y:2007:i:2:p:161-167
    DOI: 10.1140/epjb/e2006-00205-y
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    Cited by:

    1. Zhao, Pan & Pan, Jian & Yue, Qin & Zhang, Jinbo, 2021. "Pricing of financial derivatives based on the Tsallis statistical theory," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Potirakis, Stelios M. & Zitis, Pavlos I. & Eftaxias, Konstantinos, 2013. "Dynamical analogy between economical crisis and earthquake dynamics within the nonextensive statistical mechanics framework," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2940-2954.
    3. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    4. de Souza, Jeferson & Duarte Queirós, Sílvio M., 2009. "Effective multifractal features of high-frequency price fluctuations time series and ℓ-variability diagrams," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2512-2521.
    5. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
    6. Rui Pascoal & Ana Margarida Monteiro, 2013. "Market Efficiency, Roughness and Long Memory in the PSI20 Index Returns: Wavelet and Entropy Analysis," GEMF Working Papers 2013-27, GEMF, Faculty of Economics, University of Coimbra.
    7. Kozaki, M. & Sato, A.-H., 2008. "Application of the Beck model to stock markets: Value-at-Risk and portfolio risk assessment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1225-1246.
    8. Gu, Gao-Feng & Ren, Fei & Ni, Xiao-Hui & Chen, Wei & Zhou, Wei-Xing, 2010. "Empirical regularities of opening call auction in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(2), pages 278-286.
    9. Xie, Wen-Jie & Gu, Gao-Feng & Zhou, Wei-Xing, 2010. "On the growth of primary industry and population of China’s counties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3876-3882.

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