Aggregation of financial markets

Paper: arXiv 2309.04116

Authors: Georg Menz, Moritz Voß

Abstract

We present a formal framework for the aggregation of financial markets mediated by arbitrage. Our main tool is to characterize markets via utility functions and to employ a one-to-one correspondence to limit order book states. Inspired by the theory of thermodynamics, we argue that the arbitrage-mediated aggregation mechanism gives rise to a market-dynamical entropy, which quantifies the loss of liquidity caused by aggregation. As a concrete guiding example, we illustrate our general approach with the Uniswap v2 automated market maker protocol used in decentralized cryptocurrency exchanges, which we characterize as a so-called ideal market. We derive its equivalent limit order book representation and explicitly compute the arbitrage-mediated aggregation of two liquidity pools of the same asset pair with different marginal prices. We also discuss future directions of research in this emerging theory of market dynamics.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a highly novel theoretical framework mapping market aggregation and arbitrage to thermodynamic entropy, using Automated Market Makers (Uniswap v2) as a prime concrete example. While rich in mathematical formalization and theoretical depth, it lacks empirical validation or real-world transaction data backtesting.

Research Flowchart

  flowchart TD
    A[Goal: Formal framework for arbitrage-mediated financial market aggregation] --> B[Characterize markets via Utility Functions & LOB correspondence]
    C[Input: Uniswap v2 AMM Pools 'Ideal Markets' with different marginal prices] --> D[Map AMM pool states to equivalent Limit Order Books]
    B --> D
    D --> E[Compute arbitrage-mediated aggregation of liquidity pools]
    E --> F[Findings: Aggregation induces market-dynamical entropy quantifying liquidity loss]