Gauge symmetries and the Higgs mechanism in Quantum Finance

Arraut, Ivan

doi:10.1209/0295-5075/acedce

Cited by 3 publications

(1 citation statement)

References 33 publications

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“…Further theoretical insights have been provided by Arraut (2023) [11], discussing gauge symmetries and the Higgs mechanism in quantum finance, which opens up new avenues for financial theories. Additionally, Choi et al (2023) [12] from Hanyang University have emphasized the implications of quantum finance in their extensive review, broadening the academic discussion on this topic.…”

Section: Literature Reviewmentioning

confidence: 99%

Quantum Temporal Winds: Turbulence in Financial Markets

Zheng,

Dong

2024

Mathematics

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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.

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Section: Literature Reviewmentioning

confidence: 99%

Quantum Temporal Winds: Turbulence in Financial Markets

Zheng,

Dong

2024

Mathematics

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A narrative review on quantum finance theory

Dong,

Zheng,

Zhu

2024

Int. J. Quantum Inform.

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This paper systematically reviews the historical development trajectory and current situation of quantum financial theory research through an in-depth review of relevant literature. This paper summarizes the history of the concept of quantum finance, elaborates on the development stages of quantum finance, and explains the contributions of representative work in different periods in various aspects, such as theoretical frameworks, mathematical models, and algorithmic tools, which is of great significance to the research path of quantum finance. In addition, the paper introduces in detail the research progress of domestic and foreign body problems, such as quantum algorithm optimization of investment portfolios, quantitative pricing of derivatives, quantum neural networks, etc., laying a good foundation for future in-depth study of this interdisciplinary subject. Overall, this paper systematically reviews the development history of quantum finance research, provides readers with a macro understanding framework by sorting out the progress in different research fields, and has significant reference value for interdisciplinary exchanges.

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The Role of the Volatility in the Option Market

Arraut,

Lei

2023

AppliedMath

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We review some general aspects about the Black–Scholes equation, which is used for predicting the fair price of an option inside the stock market. Our analysis includes the symmetry properties of the equation and its solutions. We use the Hamiltonian formulation for this purpose. Taking into account that the volatility inside the Black–Scholes equation is a parameter, we then introduce the Merton–Garman equation, where the volatility is stochastic, and then it can be perceived as a field. We then show how the Black–Scholes equation and the Merton–Garman one are locally equivalent by imposing a gauge symmetry under changes in the prices over the Black–Scholes equation. This demonstrates that the stochastic volatility emerges naturally from symmetry arguments. Finally, we analyze the role of the volatility on the decisions taken by the holders of the options when they use the solution of the Black–Scholes equation as a tool for making investment decisions.

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Gauge symmetries and the Higgs mechanism in Quantum Finance

Cited by 3 publications

References 33 publications

Quantum Temporal Winds: Turbulence in Financial Markets

Quantum Temporal Winds: Turbulence in Financial Markets

A narrative review on quantum finance theory

The Role of the Volatility in the Option Market

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