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The probability flow in the Stock market and Spontaneous symmetry breaking in Quantum Finance

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  • Ivan Arraut
  • Joao Alexandre Lobo Marques
  • Sergio Gomes

Abstract

The Spontaneous Symmetry breaking in Quantum Finance considers the martingale condition in the stock market as a vacuum state if we express the financial equations in the Hamiltonian form. The original analysis for this phenomena ignores completely the kinetic terms in the neighborhood of the minimal of the potential terms. This is correct in most of the cases. However, when we deal with the Martingale condition, it comes out that the kinetic terms can also behave as potential terms and then reproduce a shift on the effective location of the vacuum (Martingale). In this paper we analyze the effective symmetry breaking patterns and the connected vacuum degeneracy for these special circumstances. Within the same scenario, we analyze the connection between the flow of information and the multiplicity of martingale states, providing in this way powerful tools for analyzing the dynamic of the stock market.

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  • Ivan Arraut & Joao Alexandre Lobo Marques & Sergio Gomes, 2022. "The probability flow in the Stock market and Spontaneous symmetry breaking in Quantum Finance," Papers 2206.07130, arXiv.org.
    • Handle: RePEc:arx:papers:2206.07130
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    References listed on IDEAS

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    1. Arraut, Ivan & Au, Alan & Tse, Alan Ching-biu & Segovia, Carlos, 2019. "The connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    4. Lamoureux, Christopher G & Lastrapes, William D, 1993. "Forecasting Stock-Return Variance: Toward an Understanding of Stochastic Implied Volatilities," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 293-326.
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    6. Jones, E. Philip, 1984. "Option arbitrage and strategy with large price changes," Journal of Financial Economics, Elsevier, vol. 13(1), pages 91-113, March.
    7. Ivan Arraut & Alan Au & Alan Ching-biu Tse & Carlos Segovia, 2019. "The connection between multiple prices of an Option at a given time with single prices defined at different times: The concept of weak-value in quantum finance," Papers 1905.05813, arXiv.org.
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