Related papers: G3M Impermanent Loss Dynamics
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)…
We study how trading fees and continuous-time arbitrage affect the profitability of liquidity providers (LPs) in Geometric Mean Market Makers (G3Ms). We use stochastic reflected diffusion processes to analyze the dynamics of a G3M model…
Liquidity providers are essential for the function of decentralized exchanges to ensure liquidity takers can be guaranteed a counterparty for their trades. However, liquidity providers investing in liquidity pools face many risks, the most…
AMMs are autonomous smart contracts deployed on a blockchain that make markets between different assets that live on that chain. In this paper we are examining a specific class of AMMs called Constant Function Market Makers whose trading…
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of…
We provide a framework for analyzing impermanent loss for general Automated Market Makers (AMMs) and show that Geometric Mean Market Makers (G3Ms) are in a rigorous sense the simplest class of AMMs from an impermanent loss viewpoint. In…
We consider Geometric Mean Market Makers -- a special type of Decentralized Exchange -- with two types of users: liquidity takers and arbitrageurs. Liquidity takers trade at prices that can create arbitrage opportunities, while arbitrageurs…
Uniswap is a Constant Product Market Maker built around liquidity pools, where pairs of tokens are exchanged subject to a fee that is proportional to the size of transactions. At the time of writing, there exist more than 6,000 pools…
Decentralized Finance (DeFi) is a rapidly evolving segment of blockchain technology that enables a transformative approach to financial services through Web3 applications. By leveraging smart contracts, DeFi allows developers to build…
This article analytically characterizes the impermanent loss for automatic market makers in decentralized exchanges such as Uniswap or Balancer (CPMM). We present a theoretical static replication formula for the pool value using a…
Assuming that the price in a Uniswap v3 style Automated Market Maker (AMM) follows a Geometric Brownian Motion (GBM), we prove that the strategy that adjusts the position of liquidity to track the current price leads to a deterministic and…
Constant Product Market Makers use fees that are typically fixed proportions of trade size. When these fees are automatically reinvested into the pool, as in Uniswap~V2 and some designs of Uniswap V4, the final state after a trade can…
This paper studies the question whether automated market maker protocols such as Uniswap can sustainably retain a portion of their trading fees for the protocol. We approach the problem by modelling how to optimally choose a pool's take…
In the Decentralized Finance (DeFi) setting, we present a new parametrized family of Constant Function Market Makers (CFMMs) which we call the Generalized Mean Market Makers (G3Ms), based on the generalized means. The G3Ms are intermediate…
Constant Function Market Makers (CFMMs) are a family of automated market makers that enable censorship-resistant decentralized exchange on public blockchains. Arbitrage trades have been shown to align the prices reported by CFMMs with those…
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…
This paper develops a robust mathematical framework for Constant Function Market Makers (CFMMs) by transitioning from traditional token reserve analyses to a coordinate system defined by price and intrinsic liquidity. We establish a…
This work analytically characterizes impermanent loss for automated market makers (AMMs) in decentralized markets such as Uniswap or Balancer (CPMM). We derive a static replication formula for the pool's value using a combination of…
Automated Market Makers (AMMs) are a central component of decentralized exchanges, yet their equilibrium foundations and microeconomic mechanisms remain incompletely understood. This paper develops a dynamic equilibrium framework for…
This article analytically characterizes the impermanent loss of concentrated liquidity provision for automatic market makers in decentralised markets such as Uniswap. We propose two static replication formulas for the impermanent loss by a…