  The Black-Scholes formula for pricing options on stocks and other securities
has been generalized by Merton and Garman to the case when stock volatility is
stochastic. The derivation of the price of a security derivative with
stochastic volatility is reviewed starting from the first principles of
finance. The equation of Merton and Garman is then recast using the path
integration technique of theoretical physics. The price of the stock option is
shown to be the analogue of the Schrodinger wavefuction of quantum mechacnics
and the exact Hamiltonian and Lagrangian of the system is obtained. The results
of Hull and White are generalized results for pricing stock options for the
general correlated case are derived.
