An arbitrage driven price dynamics of Automated Market Makers in the presence of fees
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929196553469952 |
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| author | Najnudel, Joseph Tung, Shen-Ning Yamazaki, Kazutoshi Yen, Ju-Yi |
| author_facet | Najnudel, Joseph Tung, Shen-Ning Yamazaki, Kazutoshi Yen, Ju-Yi |
| contents | We present a model for price dynamics in the Automated Market Makers (AMM) setting. Within this framework, we propose a reference market price following a geometric Brownian motion. The AMM price is constrained by upper and lower bounds, determined by constant multiplications of the reference price. Through the utilization of local times and excursion-theoretic approaches, we derive several analytical results, including its time-changed representation and limiting behavior. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01526 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An arbitrage driven price dynamics of Automated Market Makers in the presence of fees Najnudel, Joseph Tung, Shen-Ning Yamazaki, Kazutoshi Yen, Ju-Yi Mathematical Finance We present a model for price dynamics in the Automated Market Makers (AMM) setting. Within this framework, we propose a reference market price following a geometric Brownian motion. The AMM price is constrained by upper and lower bounds, determined by constant multiplications of the reference price. Through the utilization of local times and excursion-theoretic approaches, we derive several analytical results, including its time-changed representation and limiting behavior. |
| title | An arbitrage driven price dynamics of Automated Market Makers in the presence of fees |
| topic | Mathematical Finance |
| url | https://arxiv.org/abs/2401.01526 |