Decentralised Finance and Automated Market Making: Execution and Speculation

ArXiv ID: 2307.03499 “View on arXiv”

Authors: Unknown

Abstract

Automated market makers (AMMs) are a new prototype of decentralised exchanges which are revolutionising market interactions. The majority of AMMs are constant product markets (CPMs) where exchange rates are set by a trading function. This work studies optimal trading and statistical arbitrage in CPMs where balancing exchange rate risk and execution costs is key. Empirical evidence shows that execution costs are accurately estimated by the convexity of the trading function. These convexity costs are linear in the trade size and are nonlinear in the depth of liquidity and in the exchange rate. We develop models for when exchange rates form in a competing centralised exchange, in a CPM, or in both venues. Finally, we derive computationally efficient strategies that account for stochastic convexity costs and we showcase their out-of-sample performance.

Keywords: Automated Market Makers (AMMs), Decentralized Finance (DeFi), Constant Product Markets, Statistical Arbitrage, Convexity Costs

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced stochastic control and partial differential equations for optimal trading, and demonstrates out-of-sample performance using real market data from Uniswap and Binance.

  flowchart TD
    A["Research Goal: Optimal Trading &<br>Arbitrage in AMMs"]
    
    subgraph B ["Methodology"]
        B1["Model Exchange Rates<br>(Centralised vs CPM)"]
        B2["Quantify Convexity Costs<br>(Linear/Nonlinear)"]
        B3["Develop Stochastic<br>Optimisation Models"]
    end
    
    C["Data: Historical<br>Liquidity & Prices"]
    
    subgraph D ["Computational Process"]
        D1["Solve for Optimal<br>Execution Strategies"]
        D2["Simulate Statistical<br>Arbitrage Opportunities"]
    end
    
    subgraph E ["Key Findings"]
        E1["Convexity Costs =<br>Execution Cost Basis"]
        E2["Strategies Outperform<br>Out-of-Sample"]
    end
    
    A --> B
    B --> C
    C --> D
    D --> E