2023/09/15 by Álvaro Cartea, Cartea, Álvaro, Fayçal Drissi +3 · 1 citation
Economics, Econometrics and Finance · #14J49 (Primary) 14F60 (Secondary) #Complex Systems and Time Series Analysis #Economic theories and models #FOS: Economics and business #Financial Markets and Investment Strategies #Mathematical Finance (q-fin.MF) #Trading and Market Microstructure (q-fin.TR)
paper · pdf · doi:10.48550/arxiv.2309.08431
openalex publication_date 2023/09/15 · openalex created_date 2023/09/19 · openalex updated_date 2026/07/28
Constant product markets with concentrated liquidity (CL) are the most popular type of automated market makers. In this paper, we characterise the continuous-time wealth dynamics of strategic LPs who dynamically adjust their range of liquidity provision in CL pools. Their wealth results from fee income, the value of their holdings in the pool, and rebalancing costs. Next, we derive a self-financing and closed-form optimal liquidity provision strategy where the width of the LP's liquidity range is determined by the profitability of the pool (provision fees minus gas fees), the predictable losses (PL) of the LP's position, and concentration risk. Concentration risk refers to the decrease in fee revenue if the marginal exchange rate (akin to the midprice in a limit order book) in the pool exits the LP's range of liquidity. When the drift in the marginal rate is stochastic, we show how to optimally skew the range of liquidity to increase fee revenue and profit from the expected changes in the marginal rate. Finally, we use Uniswap v3 data to show that, on average, LPs have traded at a significant loss, and to show that the out-of-sample performance of our strategy is superior to the historical performance of LPs in the pool we consider.