Automated Market Making and Decentralized Finance

Paper: arXiv 2407.16885

Abstract

Automated market makers (AMMs) are a new type 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. Within CFMMs, we focus on constant product market makers (CPMMs) which implements the concentrated liquidity (CL) feature. In this thesis we formalise and study the trading mechanism of CPMMs with CL, and we develop liquidity provision and liquidity taking strategies. Our models are motivated and tested with market data. We derive optimal strategies for liquidity takers (LTs) who trade orders of large size and execute statistical arbitrages. First, we consider an LT who trades in a CPMM with CL and uses the dynamics of prices in competing venues as market signals. We use Uniswap v3 data to study price, liquidity, and trading cost dynamics, and to motivate the model. Next, we consider an LT who trades a basket of crypto-currencies whose constituents co-move. We use market data to study lead-lag effects, spillover effects, and causality between trading venues. We derive optimal strategies for strategic liquidity providers (LPs) who provide liquidity in CPMM with CL. First, we use stochastic control tools to 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, the dynamics of the LP’s position, and concentration risk. Next, we use a model-free approach to solve the problem of an LP who provides liquidity in multiple CPMMs with CL. We do not specify a model for the stochastic processes observed by LPs, and use a long short-term memory (LSTM) neural network to approximate the optimal liquidity provision strategy.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper employs advanced stochastic control tools (e.g., PDE-based stochastic control, closed-form derivations) and formal models for optimal liquidity provision, indicating high mathematical density. It is heavily data-driven, using Uniswap v3 market data, empirical analysis of price/liquidity dynamics, backtesting of strategies, and implementation of LSTM neural networks, demonstrating high empirical rigor.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Optimize Strategies for CPMMs with CL"] --> B["Data Collection & Analysis<br>Uniswap v3 & Crypto Market Data"]
  B --> C{"Modeling Approach"}
  C --> D["Stochastic Control<br>Optimal LP Strategy"]
  C --> E["Machine Learning<br>Model-Free LP Strategy (LSTM)"]
  D --> F["Key Findings"]
  E --> F
  F --> G["LT: Statistical Arbitrage<br>Price Dynamics & Lead-Lag Effects"]
  F --> H["LP: Self-Financing Range<br>Profitability & Concentration Risk"]

Cited References (151)

1. Optimal trading with general signals and liquidation in target zone models (2018)
2. Optimal Execution with Dynamic Order Flow Imbalance (2015)
3. Optimal liquidation under stochastic price impact (2019)
4. Incorporating order-flow into optimal execution (2016)
5. A closed-form execution strategy to target volume weighted average price (2016)
6. Algorithmic trading with model uncertainty (2017)
7. Robust strategies for optimal order execution in the Almgren–Chriss framework (2013)
8. General intensity shapes in optimal liquidation (2015)

5 of 151 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.