skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Adaptive Curves for Optimally Efficient Market Making
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.  more » « less
Award ID(s):
2325477
PAR ID:
10618773
Author(s) / Creator(s):
; ;
Editor(s):
Böhme, Rainer; Kiffer, Lucianna
Publisher / Repository:
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Date Published:
Volume:
316
ISSN:
1868-8969
ISBN:
978-3-95977-345-4
Page Range / eLocation ID:
25:1-25:22
Subject(s) / Keyword(s):
Automated market makers Adaptive Glosten-Milgrom Decentralized Finance Theory of computation → Market equilibria
Format(s):
Medium: X Size: 22 pages; 1018517 bytes Other: application/pdf
Size(s):
22 pages 1018517 bytes
Right(s):
Creative Commons Attribution 4.0 International license; info:eu-repo/semantics/openAccess
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; ; (, Proceedings of the ACM on Measurement and Analysis of Computing Systems)
    Automated marker makers (AMMs) are decentralized exchanges that enable the automated trading of digital assets. Liquidity providers (LPs) deposit digital tokens, which can be used by traders to execute trades, which generate fees for the investing LPs. In AMMs, trade prices are determined algorithmically, unlike classical limit order books. Concentrated liquidity market makers (CLMMs) are a major class of AMMs that offer liquidity providers flexibility to decide not onlyhow muchliquidity to provide, butin what ranges of pricesthey want the liquidity to be used. This flexibility can complicate strategic planning, since fee rewards are shared among LPs. We formulate and analyze a game theoretic model to study the incentives of LPs in CLMMs. Our main results show that while our original formulation admits multiple Nash equilibria and has complexity quadratic in the number of price ticks in the contract, it can be reduced to a game with a unique Nash equilibrium whose complexity is only linear. We further show that the Nash equilibrium of this simplified game follows a waterfilling strategy, in which low-budget LPs use up their full budget, but rich LPs do not. Finally, by fitting our game model to real-world CLMMs, we observe that in liquidity pools with risky assets, LPs adopt investment strategies far from the Nash equilibrium. Under price uncertainty, they generally invest in fewer and wider price ranges than our analysis suggests, with lower-frequency liquidity updates. In such risky pools, by updating their strategy to more closely match the Nash equilibrium of our game, LPs can improve their median daily returns by $116, which corresponds to an increase of 0.009% in median daily return on investment (ROI). At maximum, LPs can improve daily ROI by 0.855% when they reach Nash equilibrium. In contrast, in stable pools (e.g., of only stablecoins), LPs already adopt strategies that more closely resemble the Nash equilibrium of our game. 
    more » « less
  2. ; ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Guruswami, Venkatesan (Ed.)
    In decentralized finance ("DeFi"), automated market makers (AMMs) enable traders to programmatically exchange one asset for another. Such trades are enabled by the assets deposited by liquidity providers (LPs). The goal of this paper is to characterize and interpret the optimal (i.e., profit-maximizing) strategy of a monopolist liquidity provider, as a function of that LP’s beliefs about asset prices and trader behavior. We introduce a general framework for reasoning about AMMs based on a Bayesian-like belief inference framework, where LPs maintain an asset price estimate, which is updated by incorporating traders' price estimates. In this model, the market maker (i.e., LP) chooses a demand curve that specifies the quantity of a risky asset to be held at each dollar price. Traders arrive sequentially and submit a price bid that can be interpreted as their estimate of the risky asset price; the AMM responds to this submitted bid with an allocation of the risky asset to the trader, a payment that the trader must pay, and a revised internal estimate for the true asset price. We define an incentive-compatible (IC) AMM as one in which a trader’s optimal strategy is to submit its true estimate of the asset price, and characterize the IC AMMs as those with downward-sloping demand curves and payments defined by a formula familiar from Myerson’s optimal auction theory. We generalize Myerson’s virtual values, and characterize the profit-maximizing IC AMM. The optimal demand curve generally has a jump that can be interpreted as a "bid-ask spread," which we show is caused by a combination of adverse selection risk (dominant when the degree of information asymmetry is large) and monopoly pricing (dominant when asymmetry is small). This work opens up new research directions into the study of automated exchange mechanisms from the lens of optimal auction theory and iterative belief inference, using tools of theoretical computer science in a novel way. 
    more » « less
  3. ; ; ; (, 2nd ACM International Conference on AI in Finance (ICAIF’21))
    An index-based exchange traded fund (ETF) with underlying se- curities that trade on the same market creates potential opportu- nities for arbitrage between price deviations in the ETF and the corresponding index. We examine whether ETF arbitrage trans- mits small volatility events, termed mini flash crashes, from one of its underlying symbols to another. We address this question in an agent-based, simulated market where agents can trade an ETF and its two underlying symbols. We explore multiple market configurations with active and inactive ETF arbitrageurs. Through empirical game-theoretic analysis, we find that when arbitrageurs actively trade, background traders’ surplus increases because of the increased liquidity. Arbitrage helps the ETF more accurately track the index. We also observe that when one symbol experiences a mini flash crash, arbitrage transmits a price change in the opposite direction to the other symbol. The size of the mini flash crash de- pends more on the market configuration than the arbitrageurs, but the recovery of the mini flash crash is faster when arbitrageurs are present. 
    more » « less
  4. ; ; ; (, ACM International Conference on Artificial Intelligence in Finance)
    An index-based exchange traded fund (ETF) with underlying securities that trade on the same market creates potential opportunities for arbitrage between price deviations in the ETF and the corresponding index. We examine whether ETF arbitrage transmits small volatility events, termed mini flash crashes, from one of its underlying symbols to another. We address this question in an agent-based, simulated market where agents can trade an ETF and its two underlying symbols. We explore multiple market configurations with active and inactive ETF arbitrageurs. Through empirical game-theoretic analysis, we find that when arbitrageurs actively trade, background traders’ surplus increases because of the increased liquidity. Arbitrage helps the ETF more accurately track the index. We also observe that when one symbol experiences a mini flash crash, arbitrage transmits a price change in the opposite direction to the other symbol. The size of the mini flash crash depends more on the market configuration than the arbitrageurs, but the recovery of the mini flash crash is faster when arbitrageurs are present. 
    more » « less
  5. ; ; (, American Control Conference)
    Energy storage can generate significant revenue by taking advantage of fluctuations in real-time energy market prices. In this paper, we investigate the real-time price arbitrage potential of aerodynamic energy storage in wind farms. This under-explored source of energy storage can be realized by deferring energy extraction by turbines toward the front of a farm for later extraction by downstream turbines. In large wind farms, this kinetic energy can be stored for minutes to tens of minutes, depending on the inter-turbine travel distance and the incoming wind speed. This storage mechanism requires minimal capital costs for implementation and potentially could provide additional revenue to wind farm operators. We demonstrate that the potential for revenue generation depends on the energy arbitrage (storage) efficiency and the wind travel time between turbines. We then characterize how price volatility and arbitrage efficiency affect real-time energy market revenue potential. Simulation results show that when price volatility is low, which is the historic norm, noticeably increased revenue is only achieved with high arbitrage efficiencies. However, as price volatility increases, which is expected in the future as the composition of the power system evolves, revenues increase by several percent. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email