Automated Liquidity: Market Impact, Cycles, and De-pegging Risk
B. K. Meister
TL;DR
This paper addresses three intertwined DeFi questions: market impact under dynamic, multi-asset liquidity provisioning; a thermodynamic reinterpretation of Constant Product Market Makers; and tail-risk management for stablecoins via catastrophe bonds. It derives a generalized market impact law for OU and fractional OU price processes, showing a square-root dependence that extends to the Hurst exponent through $\Delta P = \frac{2H \hat{k}^{2H-1} \sigma^2}{k} Q^{2H-\frac{1}{2}}$. It then maps CPMMs to a crypto Carnot cycle and discusses how execution frictions limit profitability, followed by a Kelly-criterion treatment of catastrophe-bond hedges for de-pegging risk, including discrete-vs-continuous payout considerations. The results offer design insights for liquidity provision, risk management, and marketing in DeFi, particularly under policy constraints like the GENIUS Act.
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.