  The generalized 5D Black-Scholes differential equation with stochastic
volatility is derived. The projections of the stochastic evolutions associated
with the random variables from an enlarged space or superspace onto an ordinary
space can be achieved via higher-dimensional operators. The stochastic nature
of the securities and volatility associated with the 3D Merton-Garman equation
can then be interpreted as the effects of the extra dimensions. We showed that
the Merton-Garman equation is the first excited state, i.e. n=m=1, within a
family which contain an infinite numbers of Merton-Garman-like equations.
