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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.
Publication
Europhysics Letters
Volume
143
Issue
4
Pages
42001
Date
2023-08
Journal Abbr
EPL
Language
en
DOI
10.1209/0295-5075/acedce
ISSN
0295-5075
URL
https://dx.doi.org/10.1209/0295-5075/acedce
Accessed
8/18/23, 9:17 AM
Library Catalog
Institute of Physics
Extra
Publisher: EDP Sciences, IOP Publishing and Società Italiana di Fisica
Citation
Arraut, I. (2023). Gauge symmetries and the Higgs mechanism in Quantum Finance. Europhysics Letters, 143(4), 42001. https://doi.org/10.1209/0295-5075/acedce
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Link to this record
https://research.usj.edu.mo/bibliography/C2LWD8RR