Before revision:  We argue that decisions on the cost and the volume of market transactions are made under agents expectations . Random perturbations of expectations impact the market transactions and through them induce stochastic behavior of the underlying price. We derive BSM-like equation driven by Brownian motion of agents expectations . Agents expectations can be based on option trading data . We show how such expectations  can lead to  nonlinear BSM-like equations.
After revision:  We show that agents expectations can lead to nonlinear BSM-like equations.