2025/09/03 by Igor Halperin, Halperin, Igor
Computer Science · Economics, Econometrics and Finance · Physics and Astronomy · #Blockchain Technology Applications and Security #Chaos control and synchronization #Complex Systems and Time Series Analysis #Computational Physics (physics.comp-ph) #FOS: Economics and business #FOS: Physical sciences #General Finance (q-fin.GN) #Statistical Finance (q-fin.ST) #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.2509.02941
openalex publication_date 2025/09/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This work builds upon the long-standing conjecture that linear diffusion models are inadequate for complex market dynamics. Specifically, it provides experimental validation for the author's prior arguments that realistic market dynamics are governed by higher-order (cubic and higher) non-linearities in the drift. As the diffusion drift is given by the negative gradient of a potential function, this means that a non-linear drift translates into a non-quadratic potential. These arguments were based both on general theoretical grounds as well as a structured approach to modeling the price dynamics which incorporates money flows and their impact on market prices. Here, we find direct confirmation of this view by analyzing high-frequency crypto currency data at different time scales ranging from minutes to months. We find that markets can be characterized by either a single-well or a double-well potential, depending on the time period and sampling frequency, where a double-well potential may signal market uncertainty or stress.