Oracle-Parametrized Constant Function Market Makers: From Price Feeds to Pricing Rules

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.