Automated Liquidity: Market Impact, Cycles, and De-pegging Risk

Abstract: Three traits of decentralized finance are studied. First, the market impact function is derived for optimal-growth liquidity providers. For a standard random walk, the classic square-root impact is recovered. An extension is then derived to fit general fractional Ornstein-Uhlenbeck processes. These findings break with the linearized liquidity models used in most decentralized exchanges. Second, a Constant Product Market Maker is viewed as a multi-phase Carnot engine, where one phase matches the exchange of tokens by a liquidity taker, and another the change of pool size by a liquidity provider. Third, stablecoin de-pegging is a form of catastrophe risk. By using growth optimization, default odds are linked to the cost of catastrophe bonds. De-pegging insurance can act as a counterweight and a key marketing tool when the law forbids the payment of interest on stablecoins.