Paper: arXiv 2310.14320

Abstract

Constant function market makers(CFMMS) are a popular market design for decentralized exchanges(DEX). Liquidity providers(LPs) supply the CFMMs with assets to enable trades. In exchange for providing this liquidity, an LP receives a token that replicates a payoff determined by the trading function used by the CFMM. In this paper, we study a time-dependent CFMM called RMM-01. The trading function for RMM-01 is chosen such that LPs recover the payoff of a Black–Scholes priced covered call. First, we introduce the general framework for CFMMs. After, we analyze the pricing properties of RMM-01. This includes the cost of price manipulation and the corresponding implications on arbitrage. Our first primary contribution is from examining the time-varying price properties of RMM-01 and determining parameter bounds when RMM-01 has a more stable price than Uniswap. Finally, we discuss combining lending protocols with RMM-01 to achieve other option payoffs which is our other primary contribution.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 2.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents advanced mathematical derivations of trading functions, price impact, and arbitrage costs, but provides no empirical backtests, datasets, or implementation details beyond theoretical analysis.

Research Flowchart

  flowchart TD
  A["Research Goal<br/>Analyze RMM-01 CFMM Pricing & Stability"] --> B{"Methodology & Inputs"}
  B --> C["Derive Trading Function<br/>LP Payoff = Black-Scholes Covered Call"]
  B --> D["Simulation Inputs<br/>Constant liquidity, no external drift"]
  C --> E["Computational Analysis"]
  D --> E
  E --> F["Primary Outcomes"]
  F --> G["Cost of Manipulation &<br/>Arbitrage Constraints"]
  F --> H["Parameter Bounds where<br/>RMM-01 Price < Uniswap Price"]
  F --> I["Extensions<br/>Lending Integration for other Options"]