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Automated market makers: mean-variance analysis of LPs payoffs and design of pricing functions

Author

Listed:
  • Philippe Bergault

    (Université Paris Dauphine-PSL)

  • Louis Bertucci

    (Institut Louis Bachelier)

  • David Bouba

    (Swaap Labs)

  • Olivier Guéant

    (Université Paris 1 Panthéon-Sorbonne, Centre d’Economie de la Sorbonne)

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 Guéant, 2024. "Automated market makers: mean-variance analysis of LPs payoffs and design of pricing functions," Digital Finance, Springer, vol. 6(2), pages 225-247, June.
    • Handle: RePEc:spr:digfin:v:6:y:2024:i:2:d:10.1007_s42521-023-00101-0
    DOI: 10.1007/s42521-023-00101-0
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    Keywords

    Automated Market Makers; Cryptocurrencies; DeFi; Oracles; Stochastic optimal control;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • E49 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Other
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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