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Automated Market Making and Loss-Versus-Rebalancing (2208.06046v5)

Published 11 Aug 2022 in q-fin.MF, math.OC, q-fin.PM, q-fin.PR, and q-fin.TR

Abstract: We consider the market microstructure of automated market makers (AMMs) from the perspective of liquidity providers (LPs). Our central contribution is a Black-Scholes formula for AMMs''. We identify the main adverse selection cost incurred by LPs, which we callloss-versus-rebalancing'' (LVR, pronounced ``lever''). LVR captures costs incurred by AMM LPs due to stale prices that are picked off by better informed arbitrageurs. We derive closed-form expressions for LVR applicable to all automated market makers. Our model is quantitatively realistic, matching actual LP returns empirically, and shows how CFMM protocols can be redesigned to reduce or eliminate LVR.

Citations (74)

Summary

  • The paper introduces a Black-Scholes-inspired model that quantifies liquidity provider risks in automated market makers.
  • It validates the model using Uniswap v2’s WETH-USDC pair, demonstrating predictive accuracy in LP outcomes.
  • The study offers practical insights for AMM design improvements and strategies to mitigate loss-versus-rebalancing costs.

Automated Market Making and Loss-Versus-Rebalancing

This paper presents a comprehensive examination of automated market makers (AMMs), focusing particularly on the economic impacts and mechanics from the perspective of liquidity providers (LPs). At its core, the authors introduce a concept analogous to the Black-Scholes formula, which serves to elucidate the profits and losses faced by AMM LPs due to market dynamics and adversarial strategies, specifically highlighted by their "loss-versus-rebalancing" (LVR) metric.

Key Contributions

The authors detail the increasing prominence of AMMs like Uniswap in crypto markets, which have emerged as key frameworks for decentralized trading on platforms such as Ethereum. AMMs provide computational efficiency and do not necessitate active market maker participation, making them apt for decentralized exchanges (DEXs). The team's paper develops a robust model reflecting the economic realities of AMMs, delineating LP returns once market risks are counterbalanced. Central to this analysis is the LVR, an expense incurred due to arbitrage and price adjustments within AMM structures.

  1. Quantitative Model Development: The research introduces an economic model inspired by the Black-Scholes framework to analyze and predict LP outcomes in AMMs. This includes deriving formulas for LP returns that account for asset volatility and AMM-specific characteristics like marginal liquidity.
  2. Empirical Validation: One illustrative example used in the paper is the Uniswap v2 platform's WETH-USDC trading pair. The authors demonstrate the applicability and accuracy of their model by comparing predicted outcomes against actual data.
  3. Practical Insights and Applications: The paper extends its insights towards AMM design improvements, strategizing for volatility, and LVR mitigation, which is of immediate practical interest to developers and stakeholders within the AMM ecosystem.

Theoretical and Practical Implications

From a theoretical standpoint, this paper enriches the understanding of decentralized market mechanisms, presenting a structured way to assess and counterbalance the risks faced by passive LPs. Practically, the model's implications are broad: they guide the design of DEX protocols towards improved liquidity provision and advocate for integrating dynamic fee mechanisms that respond to market conditions.

The conclusion highlights avenues for future research and AMM design, focusing on the potential integration of high-frequency price oracles to reduce LVR and the strategic redistribution of arbitrage profits among LPs. These suggestions align with evolving industry practices, emphasizing a proactive approach to risk and reward management in decentralized finance.

This research underscores not only the complexities faced by LPs in AMMs but also the potential for sophisticated, data-driven models to forecast and enhance economic outcomes within the ever-dynamic blockchain trading environment. Future developments may see emphasis on refining these models with greater granularity to further incorporate live market data and machine learning predictions, thus improving real-time decision-making capabilities in AMM frameworks.

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  1. AMM - Loss vs Rebalancing (1 point, 2 comments)