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Gauge symmetries and the Higgs mechanism in Quantum Finance

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Title
Gauge symmetries and the Higgs mechanism in Quantum Finance
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.
Repository
arXiv
Archive ID
arXiv:2306.03237
Date
2023-05-09
DOI
https://doi.org/10.48550/arXiv.2306.03237
URL
http://arxiv.org/abs/2306.03237
Accessed
6/8/23, 4:45 AM
Library Catalog
arXiv.org
Extra
arXiv:2306.03237 [q-fin]
Notes
Comment: 6 pages
Citation
Arraut, I. (2023). Gauge symmetries and the Higgs mechanism in Quantum Finance (arXiv:2306.03237). arXiv. https://doi.org/https://doi.org/10.48550/arXiv.2306.03237
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https://research.usj.edu.mo/bibliography/GN6Z4C9Y