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.

6 pages

References in corpus (4)

• Spontaneous symmetry breaking in Quantum Finance
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• 5-D thermal field theory, Einstein field equations and spontaneous symmetry breaking
• Geometry, quantum correlations, and phase transitions in the $\Lambda$-atomic configuration

Cited by in corpus (1)

• On the Local equivalence of the Black Scholes and the Merton Garman equations