  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.
