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Automated Market Making and Loss-Versus-Rebalancing

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arxiv 2208.06046 v5 pith:ZCTFF5IN submitted 2022-08-11 q-fin.MF math.OCq-fin.PMq-fin.PRq-fin.TR

Automated Market Making and Loss-Versus-Rebalancing

classification q-fin.MF math.OCq-fin.PMq-fin.PRq-fin.TR
keywords marketautomatedammsincurredloss-versus-rebalancingmakersactualadverse
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We consider the market microstructure of automated market makers (AMMs) from the perspective of liquidity providers (LPs). Our central contribution is a ``Black-Scholes formula for AMMs''. We identify the main adverse selection cost incurred by LPs, which we call ``loss-versus-rebalancing'' (LVR, pronounced ``lever''). LVR captures costs incurred by AMM LPs due to stale prices that are picked off by better informed arbitrageurs. We derive closed-form expressions for LVR applicable to all automated market makers. Our model is quantitatively realistic, matching actual LP returns empirically, and shows how CFMM protocols can be redesigned to reduce or eliminate LVR.

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Cited by 24 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. From Swap Axioms to Weighted Geometric Means: A Characterization of AMMs

    cs.DC 2026-04 accept novelty 8.0 full

    Trading orbits of two-asset AMMs are level sets of weighted geometric means x^w y^{1-w} derived from validity invariance, Pareto efficiency, and unit invariance.

  2. Optimal Dynamic Fees for Automated Market Makers: A Stochastic Control Approach to Loss-Versus-Rebalancing

    q-fin.MF 2026-06 unverdicted novelty 7.0

    Derives a pro-cyclical optimal dynamic fee for AMM LPs via ergodic control that is independent of wealth and risk aversion and improves growth rate over static fees.

  3. The Privacy Subsidy: Kyle's $\lambda$ under Noise-Perturbed Order-Flow Observation

    cs.GT 2026-05 unverdicted novelty 7.0

    Derives closed-form rescaling of Kyle lambda and informed strategy under Gaussian order-flow noise, with invariant product and explicit privacy subsidy from liquidity providers to traders.

  4. The Privacy Subsidy: Kyle's $\lambda$ under Noise-Perturbed Order-Flow Observation

    cs.GT 2026-05 unverdicted novelty 7.0

    Derives closed-form Kyle equilibrium under Gaussian privacy noise on order flow, with invariant price-impact product and a privacy subsidy as the break-even fee for privacy-aggregated exchanges.

  5. The Privacy Subsidy: Kyle's $\lambda$ under Noise-Perturbed Order-Flow Observation

    cs.GT 2026-05 unverdicted novelty 7.0

    Derives closed-form linear Kyle equilibrium under Gaussian privacy noise on order flow observation, with rescaled price-impact coefficient and informed-trader strategy but invariant product, plus welfare decomposition...

  6. Funding-Aware Optimal Market Making for Perpetual DEXs

    q-fin.MF 2026-05 unverdicted novelty 7.0

    A funding-aware HJB model for perpetual DEX market making improves simulated ETH/BTC performance and reduces inventory risk versus classical Avellaneda-Stoikov.

  7. Liquidity provision in CLMMs: evidence from transactions data

    q-fin.TR 2026-04 unverdicted novelty 7.0

    Only about one in six liquidity providers in WETH/USD pools on Base avoid losses; profitable positions concentrate near the current price and are closed before the full range is crossed.

  8. ParlayMarket: Automated Market Making for Parlay-style Joint Contracts

    cs.CE 2026-03 unverdicted novelty 7.0

    ParlayMarket is the first AMM for parlay joint contracts whose repeated trading dynamics converge to the best approximation of the true joint distribution within the model class, with bounded parameter error and quadr...

  9. Amortizing Perpetual Options

    q-fin.PR 2025-12 unverdicted novelty 7.0

    Amortizing perpetual options are constructed so their pricing and exercise boundaries match those of vanilla perpetual American calls and puts on dividend-paying assets, with the amortization rate acting as the divide...

  10. Becoming Immutable: How Ethereum is Made

    econ.GN 2025-06 unverdicted novelty 7.0

    Analysis of non-winning Ethereum blocks shows 21% of user transactions are delayed and that arbitrage bot activity in the same block affects swap execution probability and price.

  11. Causal Effects of Protocol-Fee Changes on Liquidity Provision in Automated Market Makers

    stat.AP 2026-07 conditional novelty 6.0

    A matched-overlap event-study DiD of Uniswap’s protocol-fee switch finds no large short-run average LP liquidity, depth, or participation response to take-rate cuts.

  12. Proof of Stake economy under centralized exchanges--a mean field model

    q-fin.MF 2026-06 unverdicted novelty 6.0

    Mean-field game model of PoS miners acting as both validators and CEX traders; proves local well-posedness, gives semi-explicit equilibrium strategies, and numerically links centralized trading to higher staking ratio...

  13. Fairness and Strategy-Proofness in Automated Market Makers

    cs.GT 2026-06 unverdicted novelty 6.0

    For weighted-product AMMs with n≥3 assets, no aggregation rule satisfies both Arrovian fairness and strategy-proofness except single-provider dictators; the obstruction vanishes at n=2 and transfers to logarithmic opi...

  14. The Privacy Subsidy in Continuous-Time Kyle: Cumulative Welfare under Noise-Perturbed Order-Flow Observation

    cs.GT 2026-05 unverdicted novelty 6.0

    In continuous-time Kyle with privacy noise, cumulative expected transfer |Π_M| equals σ_v σ_ε² / √(σ_u² + σ_ε²) under Markovian linear equilibrium, analogous to LVR.

  15. The Privacy Subsidy in Glosten-Milgrom: Bid-Ask Spread and Welfare under Flip-Noise Direction Observation

    cs.GT 2026-05 unverdicted novelty 6.0

    In the Glosten-Milgrom model with flip-noise on trade direction, equilibrium spread equals μ(1-2η)Δ and a privacy subsidy of μηΔ transfers value from liquidity pool to traders.

  16. The Privacy Subsidy in Glosten-Milgrom: Bid-Ask Spread and Welfare under Flip-Noise Direction Observation

    cs.GT 2026-05 unverdicted novelty 6.0

    In the Glosten-Milgrom model with flip-noise on direction observation, equilibrium spread equals μ(1-2η)Δ and privacy subsidy equals μηΔ per trade.

  17. The Viability of Blockchain Markets under Discrete Clearing and Paid Priority

    q-fin.GN 2026-05 unverdicted novelty 6.0

    Blockchain markets with discrete clearing and paid priority fees experience endogenous trader selection that biases prices, impairs liquidity, and risks market shutdown as competition rises.

  18. Vault as a credit instrument

    q-fin.RM 2026-04 unverdicted novelty 6.0

    DeFi vault risk is decomposed into three levels with six on-chain mechanical features generating new loss channels, yielding five aggregated credit risk metrics and an on-chain estimation architecture.

  19. Amortizing Perpetual Options

    q-fin.PR 2025-12 unverdicted novelty 6.0

    Amortizing perpetual options are valued as equivalent vanilla perpetual American options on dividend-paying assets, with analytical formulas derived for exercise boundaries, prices, and Greeks under varying amortizati...

  20. Bounding LVR in AMMs via Secant-Tangent Divergence and Collateralized Liquidity Scaling

    cs.CE 2026-05 unverdicted novelty 5.0

    HLCP uses N-scaled virtual invariant and trigger-based collateral to reduce LVR, forming a Nash equilibrium and Pareto improvement over standard CPMM in a stylized duopoly under specific conditions.

  21. Bounding LVR in AMMs via Secant-Tangent Divergence and Collateralized Liquidity Scaling

    cs.CE 2026-05 unverdicted novelty 5.0

    HLCP uses secant-tangent divergence to trigger collateral scaling in AMMs, achieving Nash equilibrium in duopoly models and lower LVR in simulations and Uniswap data.

  22. Designing On-Chain Options: Amortizing Perpetual Options

    q-fin.MF 2026-05 unverdicted novelty 5.0

    Introduces amortizing perpetual options as a blockchain-native primitive that supports decentralized risk management including endogenous collateralization and de-peg insurance.

  23. Arbitrage and the Stability of AMM Price Tracking

    cs.CE 2026-05 unverdicted novelty 5.0

    The paper proves geometric ergodicity of AMM price tracking error under block-level arbitrage correction and derives explicit one-step bounds connecting tracking quality to liquidity and execution quality.

  24. Mitigating Adverse Selection in Concentrated Liquidity AMMs with Dynamic Fees: An Agent-Based Model Approach

    q-fin.TR 2026-06 unverdicted novelty 4.0

    Agent-based simulations of concentrated liquidity AMMs indicate that volatility- and toxicity-driven dynamic fees can raise LP fee income enough to produce positive hedged P&L in high stale-price states, compensating ...