## Quantum Neural Computation for Option Price Modelling (903)

### BibTeX

@MISC{Ivancevic903quantumneural,

author = {Vladimir G. Ivancevic},

title = {Quantum Neural Computation for Option Price Modelling},

year = {903}

}

### OpenURL

### Abstract

We propose a new generic framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a quantum linear Schrödinger equation, as a result we get a nonlinear Schrödinger 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.