Paper: arXiv 2609.33799

Authors: Hamed Amini, Zachary Feinstein

Abstract

This paper introduces oracle-parametrized automated market makers (OP-AMMs), i.e., automated market makers whose quoted price depends jointly on the pool reserves and an external oracle price. In doing so, we extend the information-agnostic AMM framework to settings, such as tokenized securities, for which price discovery occurs off-chain. Under a strict oracle-contraction condition, we show that the quoted price of any OP-AMM interpolates between the oracle price and an implicit autarkic price determined by the pool reserves. We then derive a general loss-versus-rebalancing (LVR) decomposition that separates the residual exposure to market lags from the losses induced by oracle errors. This analysis is further extended to stale, discrete-update oracles and to sandwich attacks around oracle updates. Using this framework, we find conditions under which OP-AMMs simultaneously increase local capital efficiency and reduce normalized LVR relative to information-agnostic AMMs. However, sufficiently noisy or stale oracles can reverse these gains. A counterfactual backtest using one-second SPY NBBO data is provided to demonstrate these trade-offs. In particular, we map the Pareto-efficient frontier of oracle-parametrized constant function market maker (OP-CFMM) designs across stylized oracle regimes.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: This paper presents a highly mathematical framework for Oracle-Parametrized AMMs, including axiomatic definitions and rigorous derivations. It supports its theoretical claims with a counterfactual backtest using real-world data, demonstrating a strong blend of advanced theory and empirical validation. The novelty lies in extending AMM frameworks to incorporate external oracle prices and providing a detailed LVR decomposition.

Research Flowchart

  flowchart TD
    A[Research Goal: Introduce OP-AMMs & Analyze Performance] --> B{Key Methodology: Extend AMM Framework & LVR Decomposition};
    B -- Input Data --> C[Data/Inputs: Pool Reserves, Oracle Prices (e.g., SPY NBBO 1-sec)];
    C -- Computational Processes --> D{Computational Processes: Derivations, Counterfactual Backtesting};
    D --> E[Key Findings/Outcomes: OP-AMMs interpolate prices, LVR decomposition, Conditions for improved capital efficiency & reduced LVR, Impact of noisy/stale oracles, Pareto-efficient OP-CFMM designs];