Model-Free Hedging of Impermanent Loss in Geometric Mean Market Makers with Proportional Transaction Fees

Fukasawa, Masaaki; Maire, Basile; Wunsch, Marcus

Applied Mathematical Finance, 2025, 31(2), 108-129

Number of Access:73（2025-08-14 03:52 Counts）

Identifier to cite or link to this item: https://hdl.handle.net/11094/101965

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Title
Model-Free Hedging of Impermanent Loss in Geometric Mean Market Makers with Proportional Transaction Fees
Creator
NRID
1000070506451 1000070506451
ORCID
0000-0002-0848-5001 0000-0002-0848-5001
researchmap permalink
read0140655 read0140655
Scopus Author ID
24366273400 24366273400
CreatorName
Fukasawa, Masaaki
CreatorName
Maire, Basile
CreatorName
Wunsch, Marcus
Subject
Digital currencies
decentralized finance
decentralized exchanges
automated market makers
impermanent loss
loss-versus-rebalancing
Description
This is an Accepted Manuscript of an article published by Taylor & Francis in Applied Mathematical Finance (31) on 5 Feb 2025, available at https://doi.org/10.1080/1350486X.2024.2404058.
Abstract
We consider Geometric Mean Market Makers (G3Ms)–a special type of Decentralized Exchange–with two types of traders: liquidity takers and arbitrageurs. Liquidity takers use G3Ms to swap tokens and to speculate, while arbitrageurs exploit arbitrage opportunities arising from misalignments between the G3M's price and the external market price. We show that in continuous time, a G3M charging proportional transaction fees offers exchange rates that are of finite variation, and that the opportunity cost of providing liquidity relative to rebalancing a self-financing constant-weights portfolio is, in fact, a non-negative gain. Moreover, we demonstrate that Impermanent Loss can be super-hedged in continuous time by a model-free rebalancing strategy. We conclude with a numerical analysis discussing the approximative nature of our continuous-time results for trading in discrete time.
Publisher
Routledge
Source Title
Applied Mathematical Finance
Volume (Issue)
31(2)
Page
108-129
Date of Issued
2025-02-05
Language
English
Handle URL
https://hdl.handle.net/11094/101965
PISSN
1350486X
eISSN
14664313
Relation.isVersionOf
DOI (Publisher Version)
https://doi.org/10.1080/1350486X.2024.2404058
Access Rights
embargoed access
CopyRight
This article is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
The full-text file will be made open to the public on 5 August 2026 in accordance with the publisher's policy.
oaire:version
Accepted Manuscript
Category
学術雑誌論文 Journal Article