Cryptocurrency/DeFi

Equilibrium Liquidity and Risk Offsetting in Decentralised Markets ArXiv ID: 2512.19838 “View on arXiv” Authors: Fayçal Drissi, Xuchen Wu, Sebastian Jaimungal Abstract We develop an economic model of decentralised exchanges (DEXs) in which risk-averse liquidity providers (LPs) manage risk in a centralised exchange (CEX) based on preferences, information, and trading costs. Rational, risk-averse LPs anticipate the frictions associated with replication and manage risk primarily by reducing the reserves supplied to the DEX. Greater aversion reduces the equilibrium viability of liquidity provision, resulting in thinner markets and lower trading volumes. Greater uninformed demand supports deeper liquidity, whereas higher fundamental price volatility erodes it. Finally, while moderate anticipated price changes can improve LP performance, larger changes require more intensive trading in the CEX, generate higher replication costs, and induce LPs to reduce liquidity supply. ...

A Microstructure Analysis of Coupling in CFMMs ArXiv ID: 2510.06095 “View on arXiv” Authors: Althea Sterrett, Austin Adams Abstract The programmable and composable nature of smart contract protocols has enabled the emergence of novel market structures and asset classes that are architecturally frictional to implement in traditional financial paradigms. This fluidity has produced an understudied class of market dynamics, particularly in coupled markets where one market serves as an oracle for the other. In such market structures, purchases or liquidations through the intermediate asset create coupled price action between the intermediate and final assets; leading to basket inflation or deflation when denominated in the riskless asset. This paper examines the microstructure of this inflationary dynamic given two constant function market makers (CFMMs) as the intermediate market structures; attempting to quantify their contributions to the former relative to familiar pool metrics such as price drift, trade size, and market depth. Further, a concrete case study is developed, where both markets are constant product markets. The intention is to shed light on the market design process within such coupled environments. ...

Concentrated N-dimensional AMM with Polar Coordinates in Rust ArXiv ID: 2510.05428 “View on arXiv” Authors: Vasily Tolstikov, Marcus Wentz, Joseph Schiarizzi, Derek Ding Abstract We expand on the recent development of n-dimensional automated market makers for stablecoins by showing a way to build concentrated liquidity positions with ticks in polar coordinates in Rust, including the featured ability to skew said concentrated liquidity. We highlight the risk of stacking too many stablecoin pools and how to hedge said risk. ...

Adaptive Curves for Optimally Efficient Market Making ArXiv ID: 2406.13794 “View on arXiv” Authors: Unknown Abstract Automated Market Makers (AMMs) are essential in Decentralized Finance (DeFi) as they match liquidity supply with demand. They function through liquidity providers (LPs) who deposit assets into liquidity pools. However, the asset trading prices in these pools often trail behind those in more dynamic, centralized exchanges, leading to potential arbitrage losses for LPs. This issue is tackled by adapting market maker bonding curves to trader behavior, based on the classical market microstructure model of Glosten and Milgrom. Our approach ensures a zero-profit condition for the market maker’s prices. We derive the differential equation that an optimal adaptive curve should follow to minimize arbitrage losses while remaining competitive. Solutions to this optimality equation are obtained for standard Gaussian and Lognormal price models using Kalman filtering. A key feature of our method is its ability to estimate the external market price without relying on price or loss oracles. We also provide an equivalent differential equation for the implied dynamics of canonical static bonding curves and establish conditions for their optimality. Our algorithms demonstrate robustness to changing market conditions and adversarial perturbations, and we offer an on-chain implementation using Uniswap v4 alongside off-chain AI co-processors. ...

Fees in AMMs: A quantitative study ArXiv ID: 2406.12417 “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 revenue for the AMM. We identify dynamical fees that mimic the directionality of the price due to asymmetric fee choices as a promising avenue to mitigate losses to toxic flow. This work is based on and extends a recent article by some of the authors. ...

Growth rate of liquidity provider’s wealth in G3Ms ArXiv ID: 2403.18177 “View on arXiv” Authors: Unknown Abstract 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 under the arbitrage-driven market. Our research focuses on calculating LP wealth and extends the findings of Tassy and White related to the constant product market maker (Uniswap v2) to a wider range of G3Ms, including Balancer. This allows us to calculate the long-term expected logarithmic growth of LP wealth, offering new insights into the complex dynamics of AMMs and their implications for LPs in decentralized finance. ...

Optimal Rebalancing in Dynamic AMMs ArXiv ID: 2403.18737 “View on arXiv” Authors: Unknown Abstract Dynamic AMM pools, as found in Temporal Function Market Making, rebalance their holdings to a new desired ratio (e.g. moving from being 50-50 between two assets to being 90-10 in favour of one of them) by introducing an arbitrage opportunity that disappears when their holdings are in line with their target. Structuring this arbitrage opportunity reduces to the problem of choosing the sequence of portfolio weights the pool exposes to the market via its trading function. Linear interpolation from start weights to end weights has been used to reduce the cost paid by pools to arbitrageurs to rebalance. Here we obtain the $\textit{“optimal”}$ interpolation in the limit of small weight changes (which has the downside of requiring a call to a transcendental function) and then obtain a cheap-to-compute approximation to that optimal approach that gives almost the same performance improvement. We then demonstrate this method on a range of market backtests, including simulating pool performance when trading fees are present, finding that the new approximately-optimal method of changing weights gives robust increases in pool performance. For a BTC-ETH-DAI pool from July 2022 to June 2023, the increases of pool P&L from approximately-optimal weight changes is $\sim25%$ for a range of different strategies and trading fees. ...