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Asymmetric Tsallis distributions for modeling financial market dynamics

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  • Devi, Sandhya

Abstract

Financial markets are highly non-linear and non-equilibrium systems. Earlier works have suggested that the behavior of market returns can be well described within the framework of non-extensive Tsallis statistics or superstatistics. For small time scales (delays), a good fit to the distributions of stock returns is obtained with q-Gaussian distributions, which can be derived either from Tsallis statistics or superstatistics. These distributions are symmetric. However, as the time lag increases, the distributions become increasingly non-symmetric. In this work, we address this problem by considering the data distribution as a linear combination of two independent normalized distributions — one for negative returns and one for positive returns. Each of these two independent distributions are half q-Gaussians with different non-extensivity parameter q and temperature parameter beta. Using this model, we investigate the behavior of stock market returns over time scales from 1 to 80 days. The data covers both the .com bubble and the 2008 crash periods. These investigations show that for all the time lags, the fits to the data distributions are better using asymmetric distributions than symmetric q-Gaussian distributions. The behaviors of the q parameter are quite different for positive and negative returns. For positive returns, q approaches a constant value of 1 after a certain lag, indicating the distributions have reached equilibrium. On the other hand, for negative returns, the q values do not reach a stationary value over the time scales studied. In the present model, the markets show a transition from normal to superdiffusive behavior (a possible phase transition) during the 2008 crash period. Such behavior is not observed with a symmetric q-Gaussian distribution model with q independent of time lag.

Suggested Citation

  • Devi, Sandhya, 2021. "Asymmetric Tsallis distributions for modeling financial market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    • Handle: RePEc:eee:phsmap:v:578:y:2021:i:c:s0378437121003824
    DOI: 10.1016/j.physa.2021.126109
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    References listed on IDEAS

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    1. Cortines, A.A.G. & Riera, R., 2007. "Non-extensive behavior of a stock market index at microscopic time scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 181-192.
    2. D. Sornette, 2003. "Critical Market Crashes," Papers cond-mat/0301543, arXiv.org.
    3. Michael, Fredrick & Johnson, M.D., 2003. "Financial market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 525-534.
    4. Constantino Tsallis & Celia Anteneodo & Lisa Borland & Roberto Osorio, 2003. "Nonextensive statistical mechanics and economics," Papers cond-mat/0301307, arXiv.org.
    5. Lisa Borland, 2002. "A theory of non-Gaussian option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 415-431.
    6. Lisa Borland, 2002. "A Theory of Non_Gaussian Option Pricing," Papers cond-mat/0205078, arXiv.org, revised Dec 2002.
    7. Sandhya Devi, 2019. "Financial Portfolios based on Tsallis Relative Entropy as the Risk Measure," Papers 1901.04945, arXiv.org, revised Mar 2019.
    8. Sandhya Devi, 2016. "Financial Market Dynamics: Superdiffusive or not?," Papers 1608.07752, arXiv.org, revised Sep 2017.
    9. Erik Van der Straeten & Christian Beck, 2009. "Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence," Papers 0901.2271, arXiv.org, revised Sep 2009.
    10. Xu, Dan & Beck, Christian, 2016. "Transition from lognormal to χ2-superstatistics for financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 173-183.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    12. Michael, Fredrick & Johnson, M.D., 2003. "Derivative pricing with non-linear Fokker–Planck dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 359-365.
    13. Dan Xu & Christian Beck, 2015. "Transition from lognormal to chi-square superstatistics for financial time series," Papers 1506.01660, arXiv.org, revised Mar 2016.
    14. Tsallis, Constantino & Anteneodo, Celia & Borland, Lisa & Osorio, Roberto, 2003. "Nonextensive statistical mechanics and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 89-100.
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    Cited by:

    1. Sandhya Devi & Sherman Page, 2022. "Tsallis Relative entropy from asymmetric distributions as a risk measure for financial portfolios," Papers 2205.13625, arXiv.org.
    2. Paul R. Dewick, 2022. "On Financial Distributions Modelling Methods: Application on Regression Models for Time Series," JRFM, MDPI, vol. 15(10), pages 1-15, October.
    3. Amelia Carolina Sparavigna, 2024. "Raman Spectroscopy of Siderite with q-Gaussian and split-q-Gaussian Analyses," International Journal of Sciences, Office ijSciences, vol. 13(02), pages 8-21, February.

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