Automated Market Making: the case of Pegged Assets

ArXiv ID: 2411.08145 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we introduce a novel framework to model the exchange rate dynamics between two intrinsically linked cryptoassets, such as stablecoins pegged to the same fiat currency or a liquid staking token and its associated native token. Our approach employs multi-level nested Ornstein-Uhlenbeck (OU) processes, for which we derive key properties and develop calibration and filtering techniques. Then, we design an automated market maker (AMM) model specifically tailored for the swapping of closely related cryptoassets. Distinct from existing models, our AMM leverages the unique exchange rate dynamics provided by the multi-level nested OU processes, enabling more precise risk management and enhanced liquidity provision. We validate the model through numerical simulations using real-world data for the USDC/USDT and wstETH/WETH pairs, demonstrating that it consistently yields efficient quotes. This approach offers significant potential to improve liquidity in markets for pegged assets.

Keywords: Ornstein-Uhlenbeck (OU) Processes, Automated Market Maker (AMM), Liquidity Provision, Exchange Rate Dynamics, Stablecoins, Cryptocurrencies

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 7.0/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced multi-level nested Ornstein-Uhlenbeck processes with derived properties and filtering techniques, showing high mathematical complexity. It validates the model with real-world data simulations (USDC/USDT, wstETH/WETH), demonstrating practical backtest-ready implementation.
  flowchart TD
    Start["Research Goal:<br>Model exchange rate dynamics<br>for pegged assets & design tailored AMM"] --> Inputs["Data Inputs:<br>USDC/USDT & wstETH/WETH<br>Historical Price Data"]
    Inputs --> Methodology["Methodology:<br>Multi-level Nested<br>Ornstein-Uhlenbeck Processes"]
    Methodology --> Computation["Computational Process:<br>Calibration &<br>Filtering Techniques"]
    Computation --> AMM_Design["AMM Design:<br>Leverages OU Dynamics for<br>Precise Risk Management"]
    AMM_Design --> Outcomes["Key Findings:<br>Efficient Quotes &<br>Enhanced Liquidity Provision"]
    Outcomes --> End["Conclusion:<br>Validated via Simulation<br>on Real-World Pairs"]