Aggregation of financial markets

TL;DR

This paper introduces a formal framework for aggregating financial markets through arbitrage, using thermodynamic-inspired entropy to quantify liquidity loss, exemplified by decentralized crypto exchange protocols.

Contribution

It develops a novel theoretical approach linking market aggregation, arbitrage, and entropy, with a concrete application to decentralized exchange protocols like Uniswap v2.

Findings

Derived limit order book representation for Uniswap v2

Explicitly computed arbitrage-mediated aggregation of liquidity pools

Quantified liquidity loss using market-dynamical entropy

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.