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Gauge symmetries and the Higgs mechanism in Quantum Finance

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  • Ivan Arraut

Abstract

By using the Hamiltonian formulation, we demonstrate that the Merton-Garman equation emerges naturally from the Black-Scholes equation after imposing invariance (symmetry) under local (gauge) transformations over changes in the stock price. This is the case because imposing gauge symmetry implies the appearance of an additional field, which corresponds to the stochastic volatility. The gauge symmetry then imposes some constraints over the free-parameters of the Merton-Garman Hamiltonian. Finally, we analyze how the stochastic volatility gets massive dynamically via Higgs mechanism.

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  • Ivan Arraut, 2023. "Gauge symmetries and the Higgs mechanism in Quantum Finance," Papers 2306.03237, arXiv.org.
    • Handle: RePEc:arx:papers:2306.03237
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    File URL: http://arxiv.org/pdf/2306.03237
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    Cited by:

    1. Ivan Arraut, 2024. "On the Local equivalence of the Black Scholes and the Merton Garman equations," Papers 2410.00925, arXiv.org.
    2. Haoran Zheng & Bo Dong, 2024. "Quantum Temporal Winds: Turbulence in Financial Markets," Mathematics, MDPI, vol. 12(10), pages 1-28, May.

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