Before revision:  Further we show that the Heston stochastic volatility option pricing model can be applied to our approximations and as example derive 3-dimensional BSM-like equation that describes option pricing with stochastic cost volatility and constant volume volatility.
After revision:  Further we show that the Heston stochastic volatility option pricing model can be applied to our approximations and as example derive 3-dimensional BSM-like model with stochastic value volatility and constant volume volatility.