The Case for Variable Fees in Constant Product Markets: An Agent Based Simulation

10 Pages Posted: 6 Apr 2022

See all articles by Marc Sabate-Vidales

Marc Sabate-Vidales

University of Edinburgh - School of Mathematics

David Siska

University of Edinburgh - School of Mathematics; Vega

Date Written: March 23, 2022

Abstract

We are interested in how the relationship between the fee in a constant product market (CPM) and the volatility of the swapped pair on other liquid exchanges influences the losses / gains of the liquidity providers. We review three classical market making models: Glosten and Milgrom, Kyle and Grossman and Miller and note that these very different models there is always a relationship between volatility and how rational market makers set prices. Motivated by this we set up an agent based model to explore this in the context of CPMs like Uniswap. We conclude that if the fee is too low relative to the volatility of the traded pair then the liquidity providers will end up making a loss over the medium term. From this we go to suggesting that CPM markets need to let liquidity providers set the fee via a governance mechanism especially as volatilities of assets fluctuate.

The code for all simulations is available at https://github.com/msabvid/cpm_agent_based_sim .

Keywords: DeFi, Agent-based model, Liquidity, Constant product market, Reinforcement learning, Market Microstructure

JEL Classification: C61, C63, C73, D40

Suggested Citation

Sabate-Vidales, Marc and Siska, David, The Case for Variable Fees in Constant Product Markets: An Agent Based Simulation (March 23, 2022). Available at SSRN: https://ssrn.com/abstract=4065088 or http://dx.doi.org/10.2139/ssrn.4065088

Marc Sabate-Vidales

University of Edinburgh - School of Mathematics ( email )

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

David Siska (Contact Author)

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/

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