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

TL;DR

This paper uses a quantum walk model to analyze long-term financial return distributions, capturing asymmetry and bimodality that classical models often miss.

Contribution

It introduces a quantum walk-based approach to characterize complex long-term return distributions, highlighting interference effects as a key feature.

Findings

Quantum walk model captures asymmetry and bimodality in returns.

Interference effects in quantum walks explain distribution features.

Model complements traditional short-term financial models.

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.