Decentralised Finance and Automated Market Making: Execution and Speculation

Execution and Statistical Arbitrage with Signals in Multiple Automated Market Makers

“…The authors in Cartea et al (2022a) show that one can use a Taylor expansion to approximate the execution costs for trading a quantity ∆y with the convexity of φ, so that…”

“…The literature on the optimal design of these venues and the mathematical tools to optimally take and provide liquidity are new. In Cartea et al (2022a), the authors propose models for LTs that trade in a CPMM when prices form in the pool and when the prices form in an alternative venue. In Cartea et al (2022b), the authors characterise the wealth of LPs in CFMMs and in CPMMs with concentrated liquidity, and provide dynamic LP strategies.…”

“…Key to the performance of the trading strategy, is to balance price risk and execution costs. In CPMMs, the execution costs are approximated with the convexity of the trading function, which is a function of the pool's depth and the pool's exchange rate; see Cartea et al (2022a). In our model, the joint dynamics of the CPMM rates, the oracle rates, an a set of predictive signals follow a multi-dimensional Ornstein-Uhlenbeck process (multi-OU).…”

Axioms for Automated Market Makers: A Mathematical Framework in FinTech and Decentralized Finance

“…The risks, and the appropriate hedging of those risks, for specific AMM structures have been studied in numerous works; we highlight the study of the divergence loss of Uniswap V2 [2] and Uniswap V3 [14]. (These constant product market makers were studied in a number of other works as well, e.g., [12,4].) The costs of being a liquidity provider were further analyzed within [19].…”

DeFi: Data-Driven Characterisation of Uniswap V3 Ecosystem & an Ideal Crypto Law for Liquidity Pools

“…However, concentrated liquidity also implies that LPs collect LTs' fees only while the exchange rate of executed trades lies between two ticks over which they are indeed providing liquidity. For a full characterisation of the wealth of LTs and LPs in Uniswap v3, we point to the mathematical analyses pursued in [6,7].…”