Paper: arXiv 2507.02027

Authors: Christoph Schlegel, Quintus Kilbourn

Abstract

We derive the arbitrage gains or, equivalently, Loss Versus Rebalancing (LVR) for arbitrage between \textit{“two imperfectly liquid”} markets, extending prior work that assumes the existence of an infinitely liquid reference market. Our result highlights that the LVR depends on the relative liquidity and relative trading volume of the two markets between which arbitrage gains are extracted. Our model assumes that trading costs on at least one of the markets is quadratic. This assumption holds well in practice, with the exception of highly liquid major pairs on centralized exchanges, for which we discuss extensions to other cost functions.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 4.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents advanced mathematical derivations, including stochastic calculus (GBM), quadratic cost approximations, and limit analysis to derive closed-form expressions for LVR. It is theoretically dense but lacks empirical validation, backtests, or implementation details, focusing entirely on model derivation and theoretical extensions.

Research Flowchart

  flowchart TD
  A["Research Goal: Derive arbitrage gains / LVR for<br>two imperfectly liquid markets (extending<br>reference market assumptions)"] --> B["Methodology: Quadratic Trading Cost Model<br>Assume costs quadratic on at least one market"]

  B --> C["Data/Inputs: Relative Liquidity Parameters<br>Relative Trading Volume between Markets"]

  C --> D["Computational Process: Modeling Arbitrage<br>Between Two Constrained Markets<br>Derive Closed-Form LVR Expression"]

  D --> E["Key Outcome: LVR depends on<br>Relative Liquidity & Trading Volume<br>Calibrated for Imperfect Liquidity"]

Cited References (37)

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  3. Cross-Rollup MEV: Non-Atomic Arbitrage Across L2 Blockchains (2024) — link
  4. FLAIR: A Metric for Liquidity Provider Competitiveness in Automated Market Makers (2023) — link
  5. SoK: Decentralized Exchanges (DEX) with Automated Market Maker (AMM) Protocols (2023) — link
  6. Rebalancing-versus-Rebalancing: Improving the fidelity of Loss-versus-Rebalancing (2024) — link
  7. Arbitrageurs’ profits, LVR, and sandwich attacks: batch trading as an AMM design response (2025) — link
  8. An Overview of Uniswap v4 for Researchers (2025)
and 29 more
  1. Measuring Arbitrage Losses and Profitability of AMM Liquidity (2024) — link
  2. Measuring CEX-DEX Extracted Value and Searcher Profitability: The Darkest of the MEV Dark Forest — → 2507.13023
  3. Ethereum is game-changing technology, literally. (2019) — link
  4. Automated market making and loss-versus-rebalancing (2022)
  5. Automated market making and arbitrage profits in the presence of fees — → 2305.14604
  6. Loss-Versus-Rebalancing under Deterministic and Generalized block-times — → 2505.05113
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3 of 37 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.