Automated Market Makers (AMMs) are a new prototype of
trading venues which are revolutionising the way market participants
interact. At present, the majority of AMMs are Constant Function
Market Makers (CFMMs) where a deterministic trading function
determines how markets are cleared. A distinctive characteristic of
CFMMs is that execution costs for liquidity takers, and revenue for
liquidity providers, are given by closed-form functions of price,
liquidity, and transaction size. This gives rise to a new class of
trading problems. We focus on Constant Product Market Makers with
Concentrated Liquidity and show how to optimally take and make
liquidity. We use Uniswap v3 data to study price and liquidity
dynamics and to motivate the models.
For liquidity taking, we describe how to optimally trade a large
position in an asset and how to execute statistical arbitrages based
on market signals. For liquidity provision, we show how the wealth
decomposes into a fee and an asset component. Finally, we perform
consecutive runs of in-sample estimation of model parameters and
out-of-sample trading to showcase the performance of the strategies.