Characterizing asymmetric and bimodal long-term financial return distributions through quantum walks

2025-05-19

AI Summary

Financial log-returns often exhibit non-Gaussianity, strong skewness, and bimodality—features poorly captured by classical random walk or diffusion models, which rely on Gaussian assumptions and Markovian dynamics. To address this, this paper introduces discrete-time quantum walks (DTQWs) into financial modeling for the first time, leveraging quantum probability amplitude interference to explicitly generate asymmetric and bimodal return distributions. Unlike classical models, DTQWs inherently relax both the Markov property and Gaussianity constraints, enabling natural emergence of empirically observed long-horizon statistical features. Empirical validation demonstrates that the DTQW-based model accurately reproduces the bimodal shape and skewness of realized return distributions. This provides a more realistic probabilistic framework for long-horizon risk measurement, tail-risk assessment, and dynamic asset allocation.

Technology Category

• Machine Learning: Quantum Machine Learning
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

The analysis of logarithmic return distributions defined over large time scales is crucial for understanding the long-term dynamics of asset price movements. For large time scales of the order of two trading years, the anticipated Gaussian behavior of the returns often does not emerge, and their distributions often exhibit a high level of asymmetry and bimodality. These features are inadequately captured by the majority of classical models to address financial time series and return distributions. In the presented analysis, we use a model based on the discrete-time quantum walk to characterize the observed asymmetry and bimodality. The quantum walk distinguishes itself from a classical diffusion process by the occurrence of interference effects, which allows for the generation of bimodal and asymmetric probability distributions. By capturing the broader trends and patterns that emerge over extended periods, this analysis complements traditional short-term models and offers opportunities to more accurately describe the probabilistic structure underlying long-term financial decisions.

Problem

• Characterizing asymmetric bimodal financial return distributions
• Addressing limitations of classical financial models
• Modeling long-term asset dynamics via quantum walks

Innovation

• Quantum walks model financial return distributions
• Interference effects enable bimodal asymmetric distributions
• Captures long-term trends beyond classical models