Quantum Neural Computation for Option Price Modelling

TL;DR

This paper introduces a quantum neural computation framework for option price modeling, utilizing coupled nonlinear Schrödinger equations and adaptive learning to simulate market dynamics.

Contribution

It presents a novel bidirectional quantum associative memory model for option prices, integrating quantum neural computation with adaptive Hebbian learning.

Findings

Numerical solution of coupled NLS equations demonstrates effective modeling of option dynamics.

The model captures stochastic volatility and leverage effects in option pricing.

Adaptive learning improves the model's ability to self-organize market heat potentials.

Abstract

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