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Automated Market Making and Decentralized Finance

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  • Marcello Monga

Abstract

Automated market makers (AMMs) are a new type of trading venues which are revolutionising the way market participants interact. At present, the majority of AMMs are constant function market makers (CFMMs) where a deterministic trading function determines how markets are cleared. Within CFMMs, we focus on constant product market makers (CPMMs) which implements the concentrated liquidity (CL) feature. In this thesis we formalise and study the trading mechanism of CPMMs with CL, and we develop liquidity provision and liquidity taking strategies. Our models are motivated and tested with market data. We derive optimal strategies for liquidity takers (LTs) who trade orders of large size and execute statistical arbitrages. First, we consider an LT who trades in a CPMM with CL and uses the dynamics of prices in competing venues as market signals. We use Uniswap v3 data to study price, liquidity, and trading cost dynamics, and to motivate the model. Next, we consider an LT who trades a basket of crypto-currencies whose constituents co-move. We use market data to study lead-lag effects, spillover effects, and causality between trading venues. We derive optimal strategies for strategic liquidity providers (LPs) who provide liquidity in CPMM with CL. First, we use stochastic control tools to derive a self-financing and closed-form optimal liquidity provision strategy where the width of the LP's liquidity range is determined by the profitability of the pool, the dynamics of the LP's position, and concentration risk. Next, we use a model-free approach to solve the problem of an LP who provides liquidity in multiple CPMMs with CL. We do not specify a model for the stochastic processes observed by LPs, and use a long short-term memory (LSTM) neural network to approximate the optimal liquidity provision strategy.

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  • Marcello Monga, 2024. "Automated Market Making and Decentralized Finance," Papers 2407.16885, arXiv.org.
    • Handle: RePEc:arx:papers:2407.16885
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    as
    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. Álvaro Cartea & Yixuan Wang, 2020. "Market Making With Alpha Signals," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(03), pages 1-26, May.
    3. Jonathan Chiu & Thorsten V Koeppl, 2019. "Blockchain-Based Settlement for Asset Trading," The Review of Financial Studies, Society for Financial Studies, vol. 32(5), pages 1716-1753.
    4. 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.
    5. Diebold, Francis X. & Yilmaz, Kamil, 2012. "Better to give than to receive: Predictive directional measurement of volatility spillovers," International Journal of Forecasting, Elsevier, vol. 28(1), pages 57-66.
    6. Aur'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    7. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    8. Brian Ning & Franco Ho Ting Lin & Sebastian Jaimungal, 2021. "Double Deep Q-Learning for Optimal Execution," Applied Mathematical Finance, Taylor & Francis Journals, vol. 28(4), pages 361-380, July.
    9. Natascha Hey & Jean-Philippe Bouchaud & Iacopo Mastromatteo & Johannes Muhle-Karbe & Kevin Webster, 2023. "The Cost of Misspecifying Price Impact," Papers 2306.00599, arXiv.org.
    10. Obizhaeva, Anna A. & Wang, Jiang, 2013. "Optimal trading strategy and supply/demand dynamics," Journal of Financial Markets, Elsevier, vol. 16(1), pages 1-32.
    11. 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.
    12. Guillermo Angeris & Hsien-Tang Kao & Rei Chiang & Charlie Noyes & Tarun Chitra, 2019. "An analysis of Uniswap markets," Papers 1911.03380, arXiv.org, revised Feb 2021.
    13. Álvaro Cartea & Ryan Donnelly & Sebastian Jaimungal, 2018. "Enhancing trading strategies with order book signals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 25(1), pages 1-35, January.
    14. Biais, Bruno, 1993. "Price Information and Equilibrium Liquidity in Fragmented and Centralized Markets," Journal of Finance, American Finance Association, vol. 48(1), pages 157-185, March.
    15. Lioba Heimbach & Ye Wang & Roger Wattenhofer, 2021. "Behavior of Liquidity Providers in Decentralized Exchanges," Papers 2105.13822, arXiv.org, revised Oct 2021.
    16. Alexander Barzykin & Philippe Bergault & Olivier Guéant, 2024. "Algorithmic Market Making in Spot Precious Metals," Working Papers hal-04577061, HAL.
    17. Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
    18. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    19. Martin Forde & Leandro Sánchez-Betancourt & Benjamin Smith, 2022. "Optimal trade execution for Gaussian signals with power-law resilience," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 585-596, March.
    20. Pesaran, H. Hashem & Shin, Yongcheol, 1998. "Generalized impulse response analysis in linear multivariate models," Economics Letters, Elsevier, vol. 58(1), pages 17-29, January.
    21. Tucker Hybinette Balch & Mahmoud Mahfouz & Joshua Lockhart & Maria Hybinette & David Byrd, 2019. "How to Evaluate Trading Strategies: Single Agent Market Replay or Multiple Agent Interactive Simulation?," Papers 1906.12010, arXiv.org.
    22. Philippe Bergault & Fayc{c}al Drissi & Olivier Gu'eant, 2021. "Multi-asset optimal execution and statistical arbitrage strategies under Ornstein-Uhlenbeck dynamics," Papers 2103.13773, arXiv.org, revised Mar 2022.
    23. Weston Barger & Matthew Lorig, 2019. "Optimal Liquidation Under Stochastic Price Impact," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(02), pages 1-28, March.
    24. Guillermo Angeris & Tarun Chitra & Alex Evans & Stephen Boyd, 2022. "Optimal Routing for Constant Function Market Makers," Papers 2204.05238, arXiv.org.
    25. Ryan Donnelly & Matthew Lorig, 2020. "Optimal Trading with Differing Trade Signals," Papers 2006.13585, arXiv.org, revised Oct 2020.
    26. Ryan Donnelly & Matthew Lorig, 2020. "Optimal Trading with Differing Trade Signals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(4), pages 317-344, July.
    27. Alexander Barzykin & Philippe Bergault & Olivier Guéant, 2023. "Algorithmic market making in dealer markets with hedging and market impact," Mathematical Finance, Wiley Blackwell, vol. 33(1), pages 41-79, January.
    28. 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.
    29. 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.
    30. Diego Zabaljauregui & Luciano Campi, 2019. "Optimal market making under partial information with general intensities," Papers 1902.01157, arXiv.org, revised Apr 2020.
    31. 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.
    32. Fayçal Drissi, 2022. "Solvability of Differential Riccati Equations and Applications to Algorithmic Trading with Signals," Applied Mathematical Finance, Taylor & Francis Journals, vol. 29(6), pages 457-493, November.
    33. Jason Milionis & Ciamac C. Moallemi & Tim Roughgarden, 2023. "Automated Market Making and Arbitrage Profits in the Presence of Fees," Papers 2305.14604, arXiv.org.
    34. Philippe Bergault & Fayçal Drissi & Olivier Guéant, 2022. "Multi-asset Optimal Execution and Statistical Arbitrage Strategies under Ornstein--Uhlenbeck Dynamics," Post-Print hal-03885142, HAL.
    35. Marco Avellaneda & Sasha Stoikov, 2008. "High-frequency trading in a limit order book," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 217-224.
    36. Alexander Barzykin & Philippe Bergault & Olivier Guéant, 2022. "Dealing with multi-currency inventory risk in FX cash markets," Working Papers hal-03857966, HAL.
    37. Alvaro Cartea & Luhui Gan & Sebastian Jaimungal, 2018. "Trading Cointegrated Assets with Price Impact," Papers 1807.01428, arXiv.org.
    38. Sebastian Becker & Patrick Cheridito & Arnulf Jentzen, 2019. "Pricing and hedging American-style options with deep learning," Papers 1912.11060, arXiv.org, revised Jul 2020.
    39. Glosten, Lawrence R. & Milgrom, Paul R., 1985. "Bid, ask and transaction prices in a specialist market with heterogeneously informed traders," Journal of Financial Economics, Elsevier, vol. 14(1), pages 71-100, March.
    40. Charles-Albert Lehalle & Eyal Neuman, 2019. "Incorporating signals into optimal trading," Finance and Stochastics, Springer, vol. 23(2), pages 275-311, April.
    41. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-1335, November.
    42. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    43. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    44. Philippe Bergault & Fayçal Drissi & Olivier Guéant, 2022. "Multi-asset Optimal Execution and Statistical Arbitrage Strategies under Ornstein--Uhlenbeck Dynamics," Post-Print hal-03680071, HAL.
    45. Patrick Cheridito & Tardu Sepin, 2014. "Optimal Trade Execution Under Stochastic Volatility and Liquidity," Applied Mathematical Finance, Taylor & Francis Journals, vol. 21(4), pages 342-362, September.
    46. Lioba Heimbach & Eric Schertenleib & Roger Wattenhofer, 2022. "Risks and Returns of Uniswap V3 Liquidity Providers," Papers 2205.08904, arXiv.org, revised Sep 2022.
    47. Alexander Barzykin & Philippe Bergault & Olivier Gu'eant, 2024. "Market Making in Spot Precious Metals," Papers 2404.15478, arXiv.org, revised Dec 2024.
    48. Christopher Lorenz & Alexander Schied, 2012. "Drift dependence of optimal trade execution strategies under transient price impact," Papers 1204.2716, arXiv.org, revised Mar 2013.
    49. Philippe Bergault & David Evangelista & Olivier Guéant & Douglas Vieira, 2021. "Closed-form Approximations in Multi-asset Market Making," Post-Print hal-03885121, HAL.
    50. Ryan Donnelly, 2022. "Optimal Execution: A Review," Applied Mathematical Finance, Taylor & Francis Journals, vol. 29(3), pages 181-212, May.
    51. Masaaki Fukasawa & Basile Maire & Marcus Wunsch, 2023. "Model-free Hedging of Impermanent Loss in Geometric Mean Market Makers," Papers 2303.11118, arXiv.org.
    52. Luciano Campi & Diego Zabaljauregui, 2020. "Optimal Market Making under Partial Information with General Intensities," Applied Mathematical Finance, Taylor & Francis Journals, vol. 27(1-2), pages 1-45, July.
    53. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    54. Olivier Gu'eant, 2016. "Optimal market making," Papers 1605.01862, arXiv.org, revised May 2017.
    55. Agostino Capponi & Ruizhe Jia, 2021. "The Adoption of Blockchain-based Decentralized Exchanges," Papers 2103.08842, arXiv.org, revised Jul 2021.
    56. Forsyth, P.A. & Kennedy, J.S. & Tse, S.T. & Windcliff, H., 2012. "Optimal trade execution: A mean quadratic variation approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(12), pages 1971-1991.
    57. Fischer, Thomas & Krauss, Christopher, 2018. "Deep learning with long short-term memory networks for financial market predictions," European Journal of Operational Research, Elsevier, vol. 270(2), pages 654-669.
    58. Koop, Gary & Pesaran, M. Hashem & Potter, Simon M., 1996. "Impulse response analysis in nonlinear multivariate models," Journal of Econometrics, Elsevier, vol. 74(1), pages 119-147, September.
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