Automated Market Makers Designs Beyond Constant Functions

40 Pages Posted: 25 May 2023 Last revised: 16 Aug 2023

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 in the pool of liquidity. A key drawback in the implementation of CFMs is that liquidity providers (LPs) are currently providing liquidity at a loss, on average. In this paper, we propose two new designs for decentralised trading venues, the arithmetic liquidity pool (ALP) and the geometric liquidity pool (GLP). In both pools, LPs choose impact functions that determine how liquidity taking orders impact the marginal exchange rate of the pool, and set the price of liquidity in the form of quotes around the marginal rate. The impact functions and the quotes determine the dynamics of the marginal rate and the price of liquidity. We show that CFMs are a subset of ALP; specifically, given a trading function of a CFM, there are impact functions and quotes in the ALP that replicate the marginal rate dynamics and the execution costs in the CFM. For the ALP and GLP, we propose an optimal liquidity provision strategy where the price of liquidity maximises the LP's expected profit and the strategy depends on the LP's (i) tolerance to inventory risk and (ii) views on the demand for liquidity. Our strategies admit closed-form solutions and are computationally efficient. We show that the price of liquidity in CFMs is suboptimal in the ALP. Also, we give conditions on the impact functions and the liquidity provision strategy to prevent arbitrages from rountrip trades. Finally, we use transaction data from Binance and Uniswap v3 to show that liquidity provision is not a loss-leading activity in the ALP.

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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