Optimal exit from Uniswap v3 and best expected return for a liquidity provider

Ankush Agarwal () and Emmanuel Gobet ()
Additional contact information
Ankush Agarwal: UWO - University of Western Ontario
Emmanuel Gobet: CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

Working Papers from HAL

Abstract: We analyze the profitability of liquidity providers' (LPs) positions in Uniswap v3 by aggregating fee income and impermanent loss within an optimal stopping framework. Our first result shows that liquidity burn should be optimized range by range rather than performed simultaneously. Second, without discounting, no finite optimal stopping time exists, and indefinite liquidity provision is optimal. In this regime, we derive closed-form expressions for the value of LP positions. Third, with discounting, we introduce an equivalent rate of return and demonstrate that, under a Black–Scholes model with volatility σ, the optimal return is approximately 0.425·σ2 (i.e. about 10% return for 50% volatility), and it is achieved by choosing the at-the-money range of liquidity. These results provide explicit formulas and strategic insights for LPs in Uniswap v3, and complement recent works on Uniswap v2 and fee modelling by highlighting the distinct impact of concentrated liquidity.

Keywords: automated market maker; concentrated liquidity; optimal stopping problem; best return (search for similar items in EconPapers)
Date: 2025-08-30
Note: View the original document on HAL open archive server: https://hal.science/hal-05231633v1
References: Add references at CitEc
Citations:

Downloads: (external link)
https://hal.science/hal-05231633v1/document (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:hal-05231633

Access Statistics for this paper

More papers in Working Papers from HAL
Bibliographic data for series maintained by CCSD ().