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Quantum Temporal Winds: Turbulence in Financial Markets

Author

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  • Haoran Zheng

    (School of Economics, Shanghai University, Shanghai 200444, China)

  • Bo Dong

    (School of Economics and Management, East China Normal University, Shanghai 200062, China)

Abstract

This paper leverages turbulence theory from physics to examine the similarities and differences between financial market volatility and turbulent phenomena on a statistical physics level. By drawing analogies between the dynamics of financial markets and fluid turbulence, an innovative analytical framework has been developed to enhance our understanding of the complexity inherent in financial markets. The research methodology involves a comparative analysis of several national stock market indices and simulated turbulent velocity time series, with a particular focus on key statistical properties such as probability distributions, correlation structures, and power spectral densities. Furthermore, a financial market capital flow model has been established, and corresponding solutions have been proposed. Through computational simulations and data analysis, it was discovered that financial market volatility shares some statistical characteristics with turbulence, yet there are significant differences in the shape of probability distributions and the timescales of correlations. This indicates that although financial markets exhibit patterns similar to turbulence, as a multivariate-driven complex system, their behavioral patterns do not completely correspond to natural turbulence phenomena, highlighting the limitations of directly applying turbulence theory to financial market analysis. Additionally, the study explores the use of Bézier curves to simulate market volatility and, based on these analyses, formulates trading strategies that demonstrate practical applications in risk management. This research provides fresh perspectives for the fields of financial market theory and econophysics, offering new insights into the complexity of financial markets and the prevention and management of financial risks.

Suggested Citation

  • Haoran Zheng & Bo Dong, 2024. "Quantum Temporal Winds: Turbulence in Financial Markets," Mathematics, MDPI, vol. 12(10), pages 1-28, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1416-:d:1389458
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    References listed on IDEAS

    as
    1. Ivan Arraut, 2023. "Gauge symmetries and the Higgs mechanism in Quantum Finance," Papers 2306.03237, arXiv.org.
    2. Ya-Chun Gao & Shi-Min Cai & Bing-Hong Wang, 2012. "Hierarchical structure of stock price fluctuations in financial markets," Papers 1209.4175, arXiv.org.
    3. Baaquie, Belal Ehsan, 2018. "Bonds with index-linked stochastic coupons in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 148-169.
    4. Baaquie, Belal E. & Yang, Cao, 2009. "Empirical analysis of quantum finance interest rates models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(13), pages 2666-2681.
    5. Yu Nakayama, 2009. "Gravity Dual for Reggeon Field Theory and Non-linear Quantum Finance," Papers 0906.4112, arXiv.org.
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