  This paper considers the asset price p as relations C=pV between the value C
and the volume V of the executed transactions and studies the consequences of
this definition for the option pricing equations. We show that the classical
BSM model implicitly assumes that value C and volume V of transactions follow
identical Brownian processes. Violation of this identity leads to 2-dimensional
BSM-like equation with two constant volatilities. We show that agents
expectations those approve execution of transactions can further increase the
dimension of the BSM model. We study the case when agents expectations may
depend on the option price data and show that such assumption can lead to the
nonlinear BSM-like equations. We reconsider the Heston stochastic volatility
model for the price determined by the value and the volume and derive
3-dimensional BSM-like model with stochastic value volatility and constant
volume volatility. Variety of the BSM-like equations states the problem of
reasonable balance between the accuracy and the complexity of the option
pricing equations.
