Paper: arXiv 2411.08145

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10 (capped from 7.0: no out-of-sample test; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

Cited References (53)

  1. Stablecoins and short-term funding markets (2025) — link
  2. Stablecoin devaluation risk (2025) — link
  3. Stablecoin Runs and the Centralization of Arbitrage (2025) — link
  4. Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity — → 2405.03496
  5. Market Making in Spot Precious Metals — → 2404.15478
  6. Runs and Flights to Safety: Are Stablecoins the New Money Market Funds? (2023) — link
  7. What Drives the (In)stability of a Stablecoin? (2023) — link
  8. The Cost of Misspecifying Price Impact — → 2306.00599
and 45 more
  1. Anatomy of a Run: The Terra Luna Crash (2023) — link
  2. Réglementer les émetteurs de stablecoins adossés à des actifs (2023) — link
  3. Automated market makers: mean-variance analysis of LPs payoffs and design of pricing functions — → 2212.00336
  4. A Luna-tic Stablecoin Crash (2022) — link
  5. Runs on Algorithmic Stablecoins: Evidence from Iron, Titan, and Steel (2022) — link
  6. Stablecoins: Growth Potential and Impact on Banking (2022) — link
  7. Stablecoins and Central Bank Digital Currencies: Policy and Regulatory Challenges* (2022) — link
  8. Algorithmic market making in dealer markets with hedging and market impact (2021) — link
  9. Reducing the Volatility of Cryptocurrencies - A Survey of Stablecoins (2021) — link
  10. What is Stablecoin?: A Survey on Its Mechanism and Potential as Decentralized Payment Systems (2020) — link
  11. Are stablecoins truly diversifiers, hedges, or safe havens against traditional cryptocurrencies as their name suggests? (2020) — link
  12. Stablecoins: Risks, Potential and Regulation (2020) — link
  13. The Financial Stability Board (2020) — link
  14. Global Demand for Basket-Backed Stablecoins (2020) — link
  15. While stability lasts: A stochastic model of noncustodial stablecoins (2020) — link
  16. Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality (2019) — link
  17. Size matters for OTC market makers: General results and dimensionality reduction techniques (2019) — link
  18. (In)Stability for the Blockchain: Deleveraging Spirals and Stablecoin Attacks (2019) — link
  19. Closed-form Approximations in Multi-asset Market Making (2018) — link
  20. Internalisation by electronic FX spot dealers (2018) — link
  21. Blockchains Are a Diamond’s Best Friend (2018) — link
  22. Algorithmic Trading with Model Uncertainty (2017) — link
  23. Optimal market making (2016) — link
  24. The Financial Mathematics of Market Liquidity : From Optimal Execution to Market Making (2016) — link
  25. Algorithmic and High Frequency Trading (2016) — link
  26. Buy Low, Sell High: A High Frequency Trading Perspective (2014) — link
  27. Optimal high-frequency trading with limit and market orders (2011) — link
  28. Dealing with the inventory risk: a solution to the market making problem (2011) — link
  29. High-frequency trading in a limit order book (2008) — link
  30. Numerical Procedures for Implementing Term Structure Models I (1994) — link
  31. The Dynamics of Dealer Markets Under Competition (1983) — link
  32. Optimal dealer pricing under transactions and return uncertainty (1981) — link
  33. Stablecoins: Adoption and Fragility (2023) — link
  34. Are Stablecoins the Money Market Mutual Funds of the Future? (2023) — link
  35. Taming Wildcat Stablecoins (2021) — link
  36. Decentralized Stablecoins and Collateral Risk (2021) — link
  37. NBER WORKING PAPER SERIES WHAT KEEPS STABLECOINS STABLE ? (2020)
  38. Public information and stablecoin runs
  39. Market-making by a foreign exchange dealer
  40. Can stablecoins be stable? University of Chicago, Becker
  41. How the rise of stablecoins could threaten traditional banks’ lending capacity
  42. Dealing with multi-currency inventory risk in foreign exchange cash markets
  43. § Université Paris 1 Panthéon-Sorbonne, UFR 27 Mathématiques et Informatique, Centre d’Economie de la Sorbonne, Paris, France, olivier.gueant@univ-paris1.fr. ¶ Swaap Labs, julien@swaap.finance. 1
  44. The four types of stable-coins: A comparative analysis
  45. Regulating the crypto ecosystem: the case of stablecoins and arrangements

4 of 53 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.