Automated Market Makers Designs Beyond Constant Functions

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