Execution and statistical arbitrage with signals in multiple automated market makers

Automated market makers (AMMs) are a new type of trading venue where the rules for liquidity provision and liquidity taking are considerably different from those of the traditional electronic trading venues. AMMs have become one of the key markets to trade crypto-currencies, whose liquidity is highly fragmented and prices exhibit high levels of cointegration. In this paper, we derive the optimal strategy for a liquidity taker (LT) who trades orders of large size and executes statistical arbitrages in a basket of crypto-currencies whose constituents co-move. The LT uses market signals and exchange rate information from relevant AMMs and traditional venues to enhance the performance of her strategy. We use stochastic control tools and derive a closed-form strategy that can be computed and implemented by the LT in real time. Finally, we use market data from two pools of Uniswap v3 and from the LOB-based exchange Binance to study co-movements between crypto-currencies and lead-lag effects between trading venues, and to showcase the performance of the strategy