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Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions

Author

Listed:
  • Philippe Bergault
  • Louis Bertucci
  • David Bouba
  • Olivier Gu'eant

Abstract

With the emergence of decentralized finance, new trading mechanisms called Automated Market Makers have appeared. The most popular Automated Market Makers are Constant Function Market Makers. They have been studied both theoretically and empirically. In particular, the concept of impermanent loss has emerged and explains part of the profit and loss of liquidity providers in Constant Function Market Makers. In this paper, we propose another mechanism in which price discovery does not solely rely on liquidity takers but also on an external exchange rate or price oracle. We also propose to compare the different mechanisms from the point of view of liquidity providers by using a mean / variance analysis of their profit and loss compared to that of agents holding assets outside of Automated Market Makers. In particular, inspired by Markowitz' modern portfolio theory, we manage to obtain an efficient frontier for the performance of liquidity providers in the idealized case of a perfect oracle. Beyond that idealized case, we show that even when the oracle is lagged and in the presence of adverse selection by liquidity takers and systematic arbitrageurs, optimized oracle-based mechanisms perform better than popular Constant Function Market Makers.

Suggested Citation

  • Philippe Bergault & Louis Bertucci & David Bouba & Olivier Gu'eant, 2022. "Automated Market Makers: Mean-Variance Analysis of LPs Payoffs and Design of Pricing Functions," Papers 2212.00336, arXiv.org, revised Nov 2023.
    • Handle: RePEc:arx:papers:2212.00336
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    References listed on IDEAS

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    1. Philippe Bergault & Olivier Guéant, 2021. "Size matters for OTC market makers: General results and dimensionality reduction techniques," Mathematical Finance, Wiley Blackwell, vol. 31(1), pages 279-322, January.
    2. Olivier Guéant & Iuliia Manziuk, 2019. "Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality," Post-Print hal-03252505, HAL.
    3. Fr'ed'eric Abergel & C^ome Hur'e & Huy^en Pham, 2017. "Algorithmic trading in a microstructural limit order book model," Papers 1705.01446, arXiv.org, revised Feb 2020.
    4. Olivier Gu'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.
    5. Philippe Bergault & Olivier Guéant, 2021. "Size matters for OTC market makers: General results and dimensionality reduction techniques," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03252557, HAL.
    6. Bastien Baldacci & Philippe Bergault & Olivier Guéant, 2021. "Algorithmic market making for options," Post-Print hal-03885125, HAL.
    7. Pietro Fodra & Huyên Pham, 2015. "Semi-Markov Model for Market Microstructure," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(3), pages 261-295, July.
    8. Frédéric Abergel & Côme Huré & Huyên Pham, 2020. "Algorithmic trading in a microstructural limit order book model," Post-Print hal-01514987, HAL.
    9. Philippe Bergault & Olivier Guéant, 2021. "Size matters for OTC market makers: General results and dimensionality reduction techniques," Post-Print hal-03252557, HAL.
    10. Andreas Schrimpf & Vladyslav Sushko, 2019. "FX trade execution: complex and highly fragmented," BIS Quarterly Review, Bank for International Settlements, December.
    11. Amihud, Yakov & Mendelson, Haim, 1980. "Dealership market : Market-making with inventory," Journal of Financial Economics, Elsevier, vol. 8(1), pages 31-53, March.
    12. Guillermo Angeris & Tarun Chitra, 2020. "Improved Price Oracles: Constant Function Market Makers," Papers 2003.10001, arXiv.org, revised Jun 2020.
    13. Guillermo Angeris & Tarun Chitra & Alex Evans & Stephen Boyd, 2022. "Optimal Routing for Constant Function Market Makers," Papers 2204.05238, arXiv.org.
    14. Alex Evans & Guillermo Angeris & Tarun Chitra, 2021. "Optimal Fees for Geometric Mean Market Makers," Papers 2104.00446, arXiv.org.
    15. Olivier Gu'eant & Iuliia Manziuk, 2019. "Deep reinforcement learning for market making in corporate bonds: beating the curse of dimensionality," Papers 1910.13205, arXiv.org.
    16. Philippe Bergault & David Evangelista & Olivier Guéant & Douglas Vieira, 2021. "Closed-form Approximations in Multi-asset Market Making," Applied Mathematical Finance, Taylor & Francis Journals, vol. 28(2), pages 101-142, March.
    17. Fabien Guilbaud & Huyên Pham, 2013. "Optimal high-frequency trading with limit and market orders," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 79-94, January.
    18. Ho, Thomas S Y & Stoll, Hans R, 1983. "The Dynamics of Dealer Markets under Competition," Journal of Finance, American Finance Association, vol. 38(4), pages 1053-1074, September.
    19. Andreas Schrimpf & Vladyslav Sushko, 2019. "Sizing up global foreign exchange markets," BIS Quarterly Review, Bank for International Settlements, December.
    20. O'Hara, Maureen & Oldfield, George S., 1986. "The Microeconomics of Market Making," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 21(4), pages 361-376, December.
    21. Ho, Thomas & Stoll, Hans R., 1981. "Optimal dealer pricing under transactions and return uncertainty," Journal of Financial Economics, Elsevier, vol. 9(1), pages 47-73, March.
    22. Olivier Guéant & Iuliia Manziuk, 2019. "Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03252505, HAL.
    23. Bastien Baldacci & Philippe Bergault & Olivier Guéant, 2021. "Algorithmic market making for options," Post-Print hal-03252585, HAL.
    24. Bastien Baldacci & Philippe Bergault & Olivier Guéant, 2021. "Algorithmic market making for options," Quantitative Finance, Taylor & Francis Journals, vol. 21(1), pages 85-97, January.
    25. Philippe Bergault & Olivier Guéant & David Evangelista & Douglas Vieira, 2021. "Closed-form Approximations in Multi-asset Market Making," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03680074, HAL.
    26. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    27. Olivier Guéant & Iuliia Manziuk, 2019. "Deep Reinforcement Learning for Market Making in Corporate Bonds: Beating the Curse of Dimensionality," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(5), pages 387-452, September.
    28. Vijay Mohan, 2022. "Automated market makers and decentralized exchanges: a DeFi primer," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-48, December.
    29. Philippe Bergault & Olivier Guéant & David Evangelista & Douglas Vieira, 2021. "Closed-form Approximations in Multi-asset Market Making," Post-Print hal-03680074, HAL.
    30. Stefan Loesch & Nate Hindman & Mark B Richardson & Nicholas Welch, 2021. "Impermanent Loss in Uniswap v3," Papers 2111.09192, arXiv.org.
    31. Alex Lipton & Artur Sepp, 2021. "Automated Market-Making for Fiat Currencies," Papers 2109.12196, arXiv.org.
    32. Fabien Guilbaud & Huyên Pham, 2015. "Optimal High-Frequency Trading In A Pro Rata Microstructure With Predictive Information," Mathematical Finance, Wiley Blackwell, vol. 25(3), pages 545-575, July.
    33. Alex Evans, 2020. "Liquidity Provider Returns in Geometric Mean Markets," Papers 2006.08806, arXiv.org, revised Jul 2020.
    34. Bastien Baldacci & Philippe Bergault & Olivier Guéant, 2021. "Algorithmic market making for options," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-03252585, HAL.
    35. Philippe Bergault & David Evangelista & Olivier Guéant & Douglas Vieira, 2021. "Closed-form Approximations in Multi-asset Market Making," Post-Print hal-03885121, HAL.
    36. Guillermo Angeris & Akshay Agrawal & Alex Evans & Tarun Chitra & Stephen Boyd, 2021. "Constant Function Market Makers: Multi-Asset Trades via Convex Optimization," Papers 2107.12484, arXiv.org.
    37. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    38. Pietro Fodra & Huy^en Pham, 2013. "High frequency trading and asymptotics for small risk aversion in a Markov renewal model," Papers 1310.1756, arXiv.org, revised Jan 2015.
    39. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
    40. Philippe Bergault & Olivier Guéant, 2021. "Size matters for OTC market makers: General results and dimensionality reduction techniques," Post-Print hal-03885108, HAL.
    41. Frédéric Abergel & Côme Huré & Huyên Pham, 2020. "Algorithmic trading in a microstructural limit order book model," Quantitative Finance, Taylor & Francis Journals, vol. 20(8), pages 1263-1283, August.
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    Cited by:

    1. Jason Milionis & Xin Wan & Austin Adams, 2023. "FLAIR: A Metric for Liquidity Provider Competitiveness in Automated Market Makers," Papers 2306.09421, arXiv.org.

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