Discrete-time quantum walks for modeling financial return distributions and long-term asset price dynamics

The analysis of logarithmic return distributions is crucial for understanding the dynamics of asset price movements. I explore the potential of discrete-time quantum walks to model the temporal evolution of asset prices and the resulting return distributions. When computing returns over time scales of months and years, the anticipated Gaussian behavior often does not emerge, and their distributions often exhibit a high level of asymmetry or even bimodality. These features are inadequately captured by the majority of classical models to address financial time series. A model based on the discrete-time quantum walk can be used to characterize the observed skewness 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 skewed probability distributions. By capturing the trends and patterns that emerge over extended periods, this analysis complements traditional short-term models and offers opportunities to better understand the probabilistic structure underlying long-term financial decisions.