On the potential of quantum walks for modeling financial return distributions

ArXiv ID: 2403.19502 “View on arXiv”

Authors: Unknown

Abstract

Accurate modeling of the temporal evolution of asset prices is crucial for understanding financial markets. We explore the potential of discrete-time quantum walks to model the evolution of asset prices. Return distributions obtained from a model based on the quantum walk algorithm are compared with those obtained from classical methodologies. We focus on specific limitations of the classical models, and illustrate that the quantum walk model possesses great flexibility in overcoming these. This includes the potential to generate asymmetric return distributions with complex market tendencies and higher probabilities for extreme events than in some of the classical models. Furthermore, the temporal evolution in the quantum walk possesses the potential to provide asset price dynamics.

Keywords: quantum walk, asset price evolution, discrete-time model, return distribution, extreme events, General (Asset Pricing)

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper relies on advanced quantum mechanics concepts and differential equations (like the Schrödinger equation), indicating high math complexity. However, it explicitly states that a detailed analysis against real-world data will be explored in future work, focusing on theoretical potential, which results in low empirical rigor.

  flowchart TD
    A["Research Goal:<br>Model Asset Price Evolution"] --> B["Methodology:<br>Discrete-Time Quantum Walk"]
    B --> C["Data Input:<br>Simulated Financial Data"]
    C --> D["Computational Process:<br>Generate Return Distributions"]
    D --> E["Comparison:<br>Quantum vs Classical Models"]
    E --> F["Key Finding:<br>Asymmetric Distributions"]
    E --> G["Key Finding:<br>Higher Extreme Event Probability"]
    E --> H["Key Finding:<br>Flexible Temporal Dynamics"]