2026-08-15T14:00:46Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:24725 2026-01-21T09:56:07Z ddc:004 open_access

Modeling Loss-Versus-Rebalancing in Automated Market Makers via Continuous-Installment Options Singh, Srisht Fateh Li, Reina Ke Xin Gaskin, Samuel Wu, Yuntao Klinck, Jeffrey Michalopoulos, Panagiotis Poulos, Zissis Veneris, Andreas blockchain decentralized finance automated market makers mathematical finance perpetual options continuous installments This paper mathematically models a constant-function automated market maker (CFAMM) position as a portfolio of exotic options, known as perpetual American continuous-installment (CI) options. This model replicates an AMM position’s delta at each point in time over an infinite time horizon, thus taking into account the perpetual nature and optionality to withdraw of liquidity provision. This framework yields two key theoretical results: (a) It proves that the AMM’s adverse-selection cost, loss-versus-rebalancing (LVR), is analytically identical to the continuous funding fees (the time value decay or theta) earned by the at-the-money CI option embedded in the replicating portfolio. (b) A special case of this model derives an AMM liquidity position’s delta profile and boundaries that suffer approximately constant LVR, up to a bounded residual error, over an arbitrarily long forward window. Finally, the paper describes how the constant volatility parameter required by the perpetual option can be calibrated from the term structure of implied volatilities and estimates the errors for both implied volatility calibration and LVR residual error. Thus, this work provides a practical framework enabling liquidity providers to choose an AMM liquidity profile and price boundaries for an arbitrarily long, forward-looking time window where they can expect an approximately constant, price-independent LVR. The results establish a rigorous option-theoretic interpretation of AMMs and their LVR, and provide actionable guidance for liquidity providers in estimating future adverse-selection costs and optimizing position parameters. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Srisht Fateh Singh and Reina Ke Xin Li and Samuel Gaskin and Yuntao Wu and Jeffrey Klinck and Panagiotis Michalopoulos and Zissis Poulos and Andreas Veneris 2025 Is Part Of LIPIcs, Volume 354, 7th Conference on Advances in Financial Technologies (AFT 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.AFT.2025.6 urn:nbn:de:0030-drops-247256 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AFT.2025.6 eng https://creativecommons.org/licenses/by/4.0/legalcode