Volume 143, Number 4, August 2023
|Number of page(s)||7|
|Section||Mathematical and interdisciplinary physics|
|Published online||17 August 2023|
Gauge symmetries and the Higgs mechanism in Quantum Finance
FBL, University of Saint Joseph - Estrada Marginal da Ilha Verde, 14-17, Macao, China
(a) E-mail: email@example.com (corresponding author)
Received: 28 April 2023
Accepted: 7 August 2023
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.
© 2023 EPLA
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.