Automated Market Makers (AMMs)

Price Discovery in Cryptocurrency Markets ArXiv ID: 2506.08718 “View on arXiv” Authors: Juan Plazuelo Pascual, Carlos Tardon Rubio, Juan Toro Cebada, Angel Hernando Veciana Abstract This document analyzes price discovery in cryptocurrency markets by comparing centralized and decentralized exchanges, as well as spot and futures markets. The study focuses first on Ethereum (ETH) and then applies a similar approach to Bitcoin (BTC). Chapter 1 outlines the theoretical framework, emphasizing the structural differences between centralized exchanges and decentralized finance mechanisms, especially Automated Market Makers (AMMs). It also explains how to construct an order book from a liquidity pool in a decentralized setting for comparison with centralized exchanges. Chapter 2 describes the methodological tools used: Hasbrouck’s Information Share, Gonzalo and Granger’s Permanent-Transitory decomposition, and the Hayashi-Yoshida estimator. These are applied to explore lead-lag dynamics, cointegration, and price discovery across market types. Chapter 3 presents the empirical analysis. For ETH, it compares price dynamics on Binance and Uniswap v2 over a one-year period, focusing on five key events in 2024. For BTC, it analyzes the relationship between spot and futures prices on the CME. The study estimates lead-lag effects and cointegration in both cases. Results show that centralized markets typically lead in ETH price discovery. In futures markets, while they tend to lead overall, high-volatility periods produce mixed outcomes. The findings have key implications for traders and institutions regarding liquidity, arbitrage, and market efficiency. Various metrics are used to benchmark the performance of modified AMMs and to understand the interaction between decentralized and centralized structures. ...

Loss-Versus-Rebalancing under Deterministic and Generalized block-times ArXiv ID: 2505.05113 “View on arXiv” Authors: Alex Nezlobin, Martin Tassy Abstract Although modern blockchains almost universally produce blocks at fixed intervals, existing models still lack an analytical formula for the loss-versus-rebalancing (LVR) incurred by Automated Market Makers (AMMs) liquidity providers in this setting. Leveraging tools from random walk theory, we derive the following closed-form approximation for the per block per unit of liquidity expected LVR under constant block time: [" \overline{"\mathrm{ARB"}}= \frac{",σ_b^{2"}} {",2+\sqrt{2π"},γ/(|ζ(1/2)|,σ_b),}+O!\bigl(e^{"-\mathrm{const"}\tfracγ{“σ_b”}}\bigr);\approx; \frac{“σ_b^{2”}}{",2 + 1.7164,γ/σ_b"}, "] where $σ_b$ is the intra-block asset volatility, $γ$ the AMM spread and $ζ$ the Riemann Zeta function. Our large Monte Carlo simulations show that this formula is in fact quasi-exact across practical parameter ranges. Extending our analysis to arbitrary block-time distributions as well, we demonstrate both that–under every admissible inter-block law–the probability that a block carries an arbitrage trade converges to a universal limit, and that only constant block spacing attains the asymptotically minimal LVR. This shows that constant block intervals provide the best possible protection against arbitrage for liquidity providers. ...

Automated Market Makers: Toward More Profitable Liquidity Provisioning Strategies ArXiv ID: 2501.07828 “View on arXiv” Authors: Unknown Abstract To trade tokens in cryptoeconomic systems, automated market makers (AMMs) typically rely on liquidity providers (LPs) that deposit tokens in exchange for rewards. To profit from such rewards, LPs must use effective liquidity provisioning strategies. However, LPs lack guidance for developing such strategies, which often leads them to financial losses. We developed a measurement model based on impermanent loss to analyze the influences of key parameters (i.e., liquidity pool type, position duration, position range size, and position size) of liquidity provisioning strategies on LPs’ returns. To reveal the influences of those key parameters on LPs’ profits, we used the measurement model to analyze 700 days of historical liquidity provision data of Uniswap v3. By uncovering the influences of key parameters of liquidity provisioning strategies on profitability, this work supports LPs in developing more profitable strategies. ...

Rebalancing-versus-Rebalancing: Improving the fidelity of Loss-versus-Rebalancing ArXiv ID: 2410.23404 “View on arXiv” Authors: Unknown Abstract Automated Market Makers (AMMs) hold assets and are constantly being rebalanced by external arbitrageurs to match external market prices. Loss-versus-rebalancing (LVR) is a pivotal metric for measuring how an AMM pool performs for its liquidity providers (LPs) relative to an idealised benchmark where rebalancing is done not via the action of arbitrageurs but instead by trading with a perfect centralised exchange with no fees, spread or slippage. This renders it an imperfect tool for judging rebalancing efficiency between execution platforms. We introduce Rebalancing-versus-rebalancing (RVR), a higher-fidelity model that better captures the frictions present in centralised rebalancing. We perform a battery of experiments comparing managing a portfolio on AMMs vs this new and more realistic centralised exchange benchmark-RVR. We are also particularly interested in dynamic AMMs that run strategies beyond fixed weight allocations-Temporal Function Market Makers. This is particularly important for asset managers evaluating execution management systems. In this paper we simulate more than 1000 different strategies settings as well as testing hundreds of different variations in centralised exchange (CEX) fees, AMM fees & gas costs. We find that, under this modeling approach, AMM pools (even with no retail/noise traders) often offer superior execution and rebalancing efficiency compared to centralised rebalancing, for all but the lowest CEX fee levels. We also take a simple approach to model noise traders & find that even a small amount of noise volume increases modeled AMM performance such that CEX rebalancing finds it hard to compete. This indicates that decentralised AMM-based asset management can offer superior performance and execution management for asset managers looking to rebalance portfolios, offering an alternative use case for dynamic AMMs beyond core liquidity providing. ...

Measuring Arbitrage Losses and Profitability of AMM Liquidity ArXiv ID: 2404.05803 “View on arXiv” Authors: Unknown Abstract This paper presents the results of a comprehensive empirical study of losses to arbitrageurs (following the formalization of loss-versus-rebalancing by [“Milionis et al., 2022”]) incurred by liquidity providers on automated market makers (AMMs). We show that those losses exceed the fees earned by liquidity providers across many of the largest AMM liquidity pools (on Uniswap). Remarkably, we also find that the Uniswap v2 pools are more profitable for passive LPs than their Uniswap v3 counterparts. We also investigate how arbitrage losses change with block times. As expected, arbitrage losses decrease when block production is faster. However, the rate of the decline varies significantly across different trading pairs. For instance, when comparing 100ms block times to Ethereum’s current 12-second block times, the decrease in losses to arbitrageurs ranges between 20% to 70%, depending on the specific trading pair. ...

A theoretical framework for fees in AMMs ArXiv ID: 2404.03976 “View on arXiv” Authors: Unknown Abstract In the ever evolving landscape of decentralized finance automated market makers (AMMs) play a key role: they provide a market place for trading assets in a decentralized manner. For so-called bluechip pairs, arbitrage activity provides a major part of the revenue generation of AMMs but also a major source of loss due to the so-called informed orderflow. Finding ways to minimize those losses while still keeping uninformed trading activity alive is a major problem in the field. In this paper we will investigate the mechanics of said arbitrage and try to understand how AMMs can maximize the revenue creation or in other words minimize the losses. To that end, we model the dynamics of arbitrage activity for a concrete implementation of a pool and study its sensitivity to the choice of fee aiming to maximize the value retention. We manage to map the ensuing dynamics to that of a random walk with a specific reward scheme that provides a convenient starting point for further studies. ...

Decentralized Prediction Markets and Sports Books ArXiv ID: 2307.08768 “View on arXiv” Authors: Unknown Abstract Prediction markets allow traders to bet on potential future outcomes. These markets exist for weather, political, sports, and economic forecasting. Within this work we consider a decentralized framework for prediction markets using automated market makers (AMMs). Specifically, we construct a liquidity-based AMM structure for prediction markets that, under reasonable axioms on the underlying utility function, satisfy meaningful financial properties on the cost of betting and the resulting pricing oracle. Importantly, we study how liquidity can be pooled or withdrawn from the AMM and the resulting implications to the market behavior. In considering this decentralized framework, we additionally propose financially meaningful fees that can be collected for trading to compensate the liquidity providers for their vital market function. ...

Decentralised Finance and Automated Market Making: Execution and Speculation ArXiv ID: 2307.03499 “View on arXiv” Authors: Unknown Abstract Automated market makers (AMMs) are a new prototype of decentralised exchanges which are revolutionising market interactions. The majority of AMMs are constant product markets (CPMs) where exchange rates are set by a trading function. This work studies optimal trading and statistical arbitrage in CPMs where balancing exchange rate risk and execution costs is key. Empirical evidence shows that execution costs are accurately estimated by the convexity of the trading function. These convexity costs are linear in the trade size and are nonlinear in the depth of liquidity and in the exchange rate. We develop models for when exchange rates form in a competing centralised exchange, in a CPM, or in both venues. Finally, we derive computationally efficient strategies that account for stochastic convexity costs and we showcase their out-of-sample performance. ...

FLAIR: A Metric for Liquidity Provider Competitiveness in Automated Market Makers ArXiv ID: 2306.09421 “View on arXiv” Authors: Unknown Abstract This paper aims to enhance the understanding of liquidity provider (LP) returns in automated market makers (AMMs). LPs face market risk as well as adverse selection due to risky asset holdings in the pool that they provide liquidity to and the informational asymmetry between informed traders (arbitrageurs) and AMMs. Loss-versus-rebalancing (LVR) quantifies the adverse selection cost (Milionis et al., 2022a), and is a popular metric to evaluate the flow toxicity to an AMM. However, individual LP returns are critically affected by another factor orthogonal to the above: the competitiveness among LPs. This work introduces a novel metric for LP competitiveness, called FLAIR (short for fee liquidity-adjusted instantaneous returns), that aims to supplement LVR in assessments of LP performance to capture the dynamic behavior of LPs in a pool. Our metric reflects the characteristics of fee return-on-capital, and differentiates active liquidity provisioning strategies in AMMs. To illustrate how both flow toxicity, accounting for the sophistication of the counterparty of LPs, as well as LP competitiveness, accounting for the sophistication of the competition among LPs, affect individual LP returns, we propose a quadrant interpretation where all of these characteristics may be readily visualized. We examine LP competitiveness in an ex-post fashion, and show example cases in all of which our metric confirms the expected nuances and intuition of competitiveness among LPs. FLAIR has particular merit in empirical analyses, and is able to better inform practical assessments of AMM pools. ...