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This paper studies liquid staking tokens (LSTs) on automated market makers (AMMs), both theoretically and empirically. LSTs are tokenized representations of staked assets on proof-of-stake blockchains. First, we model LST-liquidity on AMMs…

Cryptography and Security · Computer Science 2024-07-22 Krzysztof Gogol , Robin Fritsch , Malte Schlosser , Johnnatan Messias , Benjamin Kraner , Claudio Tessone

One of the exciting recent developments in decentralized finance (DeFi) has been the development of decentralized cryptocurrency exchanges that can autonomously handle conversion between different cryptocurrencies. Decentralized exchange…

Trading and Market Microstructure · Quantitative Finance 2021-01-11 Bhaskar Krishnamachari , Qi Feng , Eugenio Grippo

In decentralized finance, any individual can pool their assets into an automated market maker (AMM) -- herein we focus on the constant product market maker (CPMM) -- in exchange for a claim on a fraction of future pool assets and fees…

Mathematical Finance · Quantitative Finance 2026-01-27 Maxim Bichuch , Zachary Feinstein

We study liquidity on decentralized exchanges (DEXs), identifying factors at the platform, blockchain, token pair, and liquidity pool levels with predictive power for market depth metrics. We introduce the v2 counterfactual spread metric, a…

Trading and Market Microstructure · Quantitative Finance 2025-01-20 Brian Z. Zhu , Dingyue Liu , Xin Wan , Gordon Liao , Ciamac C. Moallemi , Brad Bachu

Geometric mean market makers (G3Ms), such as Uniswap and Balancer, comprise a popular class of automated market makers (AMMs) defined by the following rule: the reserves of the AMM before and after each trade must have the same (weighted)…

Mathematical Finance · Quantitative Finance 2020-07-16 Alex Evans

We introduce a class of utility-based market makers that always accept orders at their risk-neutral prices. We derive necessary and sufficient conditions for such market makers to have bounded loss. We prove that hyperbolic absolute risk…

Computer Science and Game Theory · Computer Science 2012-10-16 Yiling Chen , David M Pennock

We examine how the introduction of concentrated liquidity has changed the liquidity provision market in automated market makers such as Uniswap. To this end, we compare average liquidity provider returns from trading fees before and after…

Trading and Market Microstructure · Quantitative Finance 2023-10-30 Robin Fritsch

In traditional finance, the Black & Scholes model has guided almost 50 years of derivatives pricing, defining a standard to model any volatility-based product. With the rise of Decentralized Finance (DeFi) and constant product Automated…

Mathematical Finance · Quantitative Finance 2023-03-13 Niccolò Bardoscia , Alessandro Nodari

Concentrated Liquidity Market Makers (CLMMs) represent a fundamental innovation in market microstructure, transforming liquidity provision from passive portfolio allocation to active risk management. This evolution creates significant…

Mathematical Finance · Quantitative Finance 2026-03-31 Andrey Urusov , Rostislav Berezovskiy , Anatoly Krestenko , Andrei Kornilov , Yury Yanovich

Decentralized finance (DeFi) has revolutionized the financial landscape, with protocols like Uniswap offering innovative automated market-making mechanisms. This article explores the development of a backtesting framework specifically…

Mathematical Finance · Quantitative Finance 2024-10-15 Andrey Urusov , Rostislav Berezovskiy , Yury Yanovich

Large deployment of distribute energy resources and the increasing awareness of end-users towards their energy procurement are challenging current practices of electricity markets. A change of paradigm, from a top-down hierarchical approach…

Optimization and Control · Mathematics 2020-09-18 Fabio Moret , Andrea Tosatto , Thomas Baroche , Pierre Pinson

Decentralized exchanges (DEXs) provide a means for users to trade pairs of assets on-chain without the need for a trusted third party to effectuate a trade. Amongst these, constant function market maker DEXs such as Uniswap handle the most…

Computer Science and Game Theory · Computer Science 2022-08-29 Zhou Fan , Francisco Marmolejo-Cossío , Ben Altschuler , He Sun , Xintong Wang , David C. Parkes

Passive liquidity providers (LPs) in automated market makers (AMMs) face losses due to adverse selection (LVR), which static trading fees often fail to offset in practice. We study the key determinants of LP profitability in a dynamic…

Trading and Market Microstructure · Quantitative Finance 2025-08-12 Steven Campbell , Philippe Bergault , Jason Milionis , Marcel Nutz

The emergence of Concentrated Liquidity Market Makers (CLMMs) has made liquidity provision on decentralized exchanges an active and risk-sensitive task. However, the standalone profitability of liquidity provision remains unclear for…

Trading and Market Microstructure · Quantitative Finance 2026-04-27 Andrey Urusov , Rostislav Berezovskiy , Anatoly Krestenko , Andrei Kornilov

The trustless nature of permissionless blockchains renders overcollateralization a key safety component relied upon by decentralized finance (DeFi) protocols. Nonetheless, factors such as price volatility may undermine this mechanism. In…

General Finance · Quantitative Finance 2021-12-14 Daniel Perez , Sam M. Werner , Jiahua Xu , Benjamin Livshits

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…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-04-23 Robin Fritsch , Andrea Canidio

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…

Statistical Finance · Quantitative Finance 2025-05-16 Abe Alexander , Lars Fritz

We investigate whether the fee income from trades on the CFM is sufficient for the liquidity providers to hedge away the exposure to market risk. We first analyse this problem through the lens of continuous-time financial mathematics and…

Mathematical Finance · Quantitative Finance 2023-02-10 Samuel Cohen , Marc Sabaté Vidales , David Šiška , Łukasz Szpruch

We consider an illiquid financial market where a risk averse investor has to liquidate a portfolio within a finite time horizon [0,T] and can trade continuously at a traditional exchange (the "primary venue") and in a dark pool. At the…

Trading and Market Microstructure · Quantitative Finance 2012-08-07 Peter Kratz , Torsten Schöneborn

We investigate the market microstructure of Automated Market Makers (AMMs), the most prominent type of blockchain-based decentralized exchanges. We show that the order execution mechanism yields token value loss for liquidity providers if…

Trading and Market Microstructure · Quantitative Finance 2021-07-22 Agostino Capponi , Ruizhe Jia