Non-Linear and Meta-Stable Dynamics in Financial Markets: Evidence from High Frequency Crypto Currency Market Makers
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909768159854592 |
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| author | Halperin, Igor |
| author_facet | Halperin, Igor |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_02941 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Linear and Meta-Stable Dynamics in Financial Markets: Evidence from High Frequency Crypto Currency Market Makers Halperin, Igor Statistical Finance Computational Physics General Finance Trading and Market Microstructure 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. |
| title | Non-Linear and Meta-Stable Dynamics in Financial Markets: Evidence from High Frequency Crypto Currency Market Makers |
| topic | Statistical Finance Computational Physics General Finance Trading and Market Microstructure |
| url | https://arxiv.org/abs/2509.02941 |