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arXiv · 2401.01526

An arbitrage driven price dynamics of Automated Market Makers in the presence of fees

Joseph Najnudel·Shen-Ning Tung·Kazutoshi Yamazaki·Ju-Yi Yen
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Abstract

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.

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Joseph Najnudel, Shen-Ning Tung, Kazutoshi Yamazaki, Ju-Yi Yen. 2024-01-03. An arbitrage driven price dynamics of Automated Market Makers in the presence of fees. https://arxiv.org/abs/2401.01526

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