Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity

ArXiv ID: 2405.03496 “View on arXiv”

Authors: Unknown

Abstract

In this paper, we introduce a suite of models for price-aware automated market making platforms willing to optimize their quotes. These models incorporate advanced price dynamics, including stochastic volatility, jumps, and microstructural price models based on Hawkes processes. Additionally, we address the variability in demand from liquidity takers through models that employ either Hawkes or Markov-modulated Poisson processes. Each model is analyzed with particular emphasis placed on the complexity of the numerical methods required to compute optimal quotes.

Keywords: market making, Hawkes processes, stochastic volatility, optimal quoting, optimal execution

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats
• Why: The paper is mathematically dense, featuring advanced stochastic processes (Heston-Bates, Stein-Stein, Hawkes, Markov-modulated Poisson) and nonlinear PDEs, but lacks empirical validation, backtests, or code; it focuses purely on theoretical model formulation and numerical method complexity.

  flowchart TD
    A["Research Goal:<br>Develop Price-Aware AMM Models<br>for Optimal Quoting"] --> B["Methodology:<br>Integrate Advanced Price Dynamics"]
    B --> C{"Input: Asset Price Models"}
    C --> D["Stochastic Volatility<br>Models"]
    C --> E["Jump-Diffusion<br>Models"]
    C --> F["Hawkes Process<br>Microstructure Models"]
    
    B --> G{"Input: Demand Models"}
    G --> H["Hawkes Process<br>Order Flow"]
    G --> I["Markov-Modulated<br>Poisson Process"]
    
    D & E & F & H & I --> J["Computational Process:<br>Numerical Methods for<br>Optimal Quote Calculation"]
    
    J --> K{"Key Findings/Outcomes"}
    K --> L["Model-Specific<br>Numerical Complexity"]
    K --> M["Optimal Quoting<br>Strategies"]
    K --> N["Framework for<br>Price-Aware AMM Optimization"]