Strategic Bonding Curves in Automated Market Makers

Abstract

The bonding curves of decentralised exchanges (DEXs) define, with mathematical formulae, the relationship between liquidity supply, price impact, and execution prices. Most DEXs use the bonding curves of constant function markets (CFMs) to clear the supply and demand of liquidity. At present, liquidity providers (LPs) operate at a loss in CFMs, on average. We generalise CFMs and introduce decentralised liquidity pools (DLPs) which provide LPs with the tools to design dynamic bonding curves according to strategic preferences. In DLPs, impact functions  encode how orders affect prices and quote functions  encode how the price of liquidity is determined. To illustrate the strategic flexibility of LPs in DLPs, we develop models for dynamic bonding curves when prices form in a competing trading venue, within  the DLP, or across multiple venues. In  fragmented markets, the DLP estimates the fundamental price from the trading flow to adjust the bonding curve and reduce arbitrage losses. Our models may be used as hooks in Uniswap v4 when the DLP's impact functions are those implied by the constant product function.

Keywords: decentralised finance, automated market making, smart contracts, algorithmic trading, market making, stochastic AMMs, Uniswap v4, hooks