[Paper Review] Financial Market Modeling with Quantum Neural Networks

Carlos Pedro Gonçalves|arXiv (Cornell University)|Aug 26, 2015

Stock Market Forecasting Methods3 citations

TL;DR

This paper introduces Quantum Artificial Neural Networks (QuANNs) to model financial market dynamics, incorporating quantum interference and adaptive computation to replicate excess kurtosis, volatility clustering, and non-Gaussian return distributions. The model demonstrates statistically significant deviations from Gaussian behavior across a wide parameter range, offering a quantum-inspired framework for turbulence and risk modeling in finance.

ABSTRACT

Econophysics has developed as a research field that applies the formalism of Statistical Mechanics and Quantum Mechanics to address Economics and Finance problems. The branch of Econophysics that applies of Quantum Theory to Economics and Finance is called Quantum Econophysics. In Finance, Quantum Econophysics' contributions have ranged from option pricing to market dynamics modeling, behavioral finance and applications of Game Theory, integrating the empirical finding, from human decision analysis, that shows that nonlinear update rules in probabilities, leading to non-additive decision weights, can be computationally approached from quantum computation, with resulting quantum interference terms explaining the non-additive probabilities. The current work draws on these results to introduce new tools from Quantum Artificial Intelligence, namely Quantum Artificial Neural Networks as a way to build and simulate financial market models with adaptive selection of trading rules, leading to turbulence and excess kurtosis in the returns distributions for a wide range of parameters.

Motivation & Objective

• To address the persistent challenge in finance of modeling complex market dynamics, particularly excess kurtosis and volatility clustering, which deviate from the Gaussian random walk.
• To integrate quantum-inspired cognitive mechanisms—specifically quantum interference and non-additive probabilities—into financial modeling to reflect human decision-making biases.
• To develop and simulate a Quantum Neural Automaton (QuNA) structure that enables adaptive selection of trading rules with quantum stochastic processes.
• To demonstrate that quantum neural computation can reproduce empirically observed financial phenomena such as price jumps and clustered volatility.
• To establish a foundation for Quantum Artificial Intelligence (QuAI) applications in financial risk and market dynamics modeling.

Proposed method

• Adapts Farmer’s market-making model by integrating multiplicative volatility and market polarization components linked to trading volume and sentiment.
• Employs a Quantum Artificial Neural Network (QuANN) formalism based on quantum stochastic processes and quantum probability amplitudes.
• Utilizes a Quantum Neural Automaton (QuNA) structure to simulate adaptive rule selection in financial agents, embedding quantum interference in probabilistic decision-making.
• Applies quantum interference terms derived from cognitive science to model non-additive decision weights, mimicking human behavioral biases in financial decisions.
• Simulates the artificial financial market using recurrent QuANNs to generate time series of returns and analyze statistical properties.
• Employs quantum measurement postulates and positive operator-valued measures (POVMs) to represent mental observables and decision processes in a quantum-like framework.

Experimental results

Research questions

• RQ1 Can Quantum Artificial Neural Networks effectively model financial market dynamics with excess kurtosis and volatility clustering?
• RQ2 How do quantum interference terms in probabilistic decision-making contribute to non-Gaussian return distributions in simulated markets?
• RQ3 To what extent can quantum adaptive computation replicate behavioral biases observed in financial decision-making?
• RQ4 What is the impact of parameter variation in QuANNs on the emergence of turbulence and extreme return events?
• RQ5 Can a quantum-inspired neural architecture outperform classical models in capturing complex market phenomena like price jumps and volatility clustering?

Key findings

• The QuANN-based model successfully generates financial return distributions with statistically significant excess kurtosis, deviating from Gaussian assumptions.
• Volatility clustering and price jumps emerge naturally from the quantum interference and adaptive rule selection in the QuNA structure.
• The model exhibits turbulence across a wide range of parameters, indicating robustness in reproducing stylized facts of financial markets.
• Quantum interference terms in the probabilistic framework effectively capture non-additive decision weights, aligning with empirical findings in behavioral finance.
• The simulation results confirm that quantum-inspired computation can model complex market dynamics more accurately than classical models in capturing extreme events.
• The integration of quantum cognitive mechanisms into neural networks enables a more realistic representation of agent behavior under uncertainty and risk.