Automated Market Makers Designs Beyond Constant Functions

34 Pages Posted: 25 May 2023 Last revised: 17 Apr 2024

See all articles by Álvaro Cartea

Álvaro Cartea

University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

Fayçal Drissi

University of Oxford - Oxford-Man Institute of Quantitative Finance

Leandro Sánchez-Betancourt

Mathematical Institute, University of Oxford; University of Oxford - Oxford-Man Institute of Quantitative Finance

David Siska

University of Edinburgh - School of Mathematics; Vega

Lukasz Szpruch

University of Edinburgh - School of Mathematics; The Alan Turing Institute; Simtopia

Date Written: May 25, 2023

Abstract

Popular automated market makers (AMMs) use constant function markets (CFMs) to clear the demand and supply of liquidity. A key drawback of CFMs is that liquidity providers (LPs) are currently providing liquidity at a loss, on average. This paper proposes a new design for decentralised trading venues, called the arithmetic liquidity pool (ALP), in which LPs are given the tools to behave strategically. The ALP uses (i) impact functions that determine how liquidity taking orders impact the marginal exchange rate of the pool, and (ii) quote functions that determine the price of liquidity in the form of dynamic quotes around the marginal rate of the pool. We derive conditions to prevent arbitrages from round-trip trades in the ALP, and we demonstrate that CFMs are a subset of ALP; specifically, there are impact functions and quotes in the ALP that replicate the CFM for any trading function. We show that the predictable losses of LPs in CFMs can be prevented with strategic liquidity provision in the ALP. Finally, we propose a family of computationally efficient closed-form ALP strategies where the price of liquidity maximises the expected profit of LPs based on assumptions over the demand for liquidity and future exchange rates. Transaction data from Binance and Uniswap v3 are used to show that liquidity provision is not a loss-leading activity in an ALP that implements our strategy.

Keywords: decentralised finance, automated market making, smart contracts, algorithmic trading, market making, stochastic AMMs

Suggested Citation

Cartea, Álvaro and Drissi, Fayçal and Sánchez-Betancourt, Leandro and Siska, David and Szpruch, Lukasz, Automated Market Makers Designs Beyond Constant Functions (May 25, 2023). Available at SSRN: https://ssrn.com/abstract=4459177 or http://dx.doi.org/10.2139/ssrn.4459177

Álvaro Cartea

University of Oxford ( email )

Mansfield Road
Oxford, Oxfordshire OX1 4AU
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Fayçal Drissi (Contact Author)

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

Leandro Sánchez-Betancourt

Mathematical Institute, University of Oxford ( email )

Andrew Wiles Building
Woodstock Road
Oxford, Oxfordshire OX2 6GG
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

Eagle House
Walton Well Road
Oxford, Oxfordshire OX2 6ED
United Kingdom

David Siska

University of Edinburgh - School of Mathematics ( email )

United Kingdom

HOME PAGE: http://https://www.maths.ed.ac.uk/~dsiska/

Vega ( email )

Vega Holdings Limited
Suite 23 Portland House, Glacis Road
Gibraltar, GX11 1AA
Gibraltar

HOME PAGE: http://vega.xyz/

Lukasz Szpruch

University of Edinburgh - School of Mathematics ( email )

James Clerk Maxwell Building
Peter Guthrie Tait Rd
Edinburgh, EH9 3FD
United Kingdom

The Alan Turing Institute ( email )

British Library, 96 Euston Road
96 Euston Road
London, NW12DB
United Kingdom

Simtopia ( email )

United Kingdom

HOME PAGE: http://https://www.simtopia.ai

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