  We propose a new cognitive framework for option price modelling, using
quantum neural computation formalism. Briefly, when we apply a classical
nonlinear neural-network learning to a linear quantum Schr\"odinger equation,
as a result we get a nonlinear Schr\"odinger equation (NLS), performing as a
quantum stochastic filter. In this paper, we present a bidirectional quantum
associative memory model for the Black--Scholes--like option price evolution,
consisting of a pair of coupled NLS equations, one governing the stochastic
volatility and the other governing the option price, both self-organizing in an
adaptive `market heat potential', trained by continuous Hebbian learning. This
stiff pair of NLS equations is numerically solved using the method of lines
with adaptive step-size integrator.
  Keywords: Option price modelling, Quantum neural computation, nonlinear
Schr\"odinger equations, leverage effect, bidirectional associative memory
