A central question of the Ethereum ecosystem is where Maximal Extractable Value (MEV)revenue originates and to what extent it stems from harming unsuspecting users. It is acceptable if MEV arises from arbitrages between centralised and decentralised exchanges (CEX-DEX). Yet theoretical models have significantly underestimated the scale of these arbitrages, while empirical studies have highlighted their importance - though these remain conservative estimates, constrained by numerous debatable heuristic assumptions. Revisiting the theoretical model, we found that CEX-DEX arbitrages require trading volumes on the order of the total activity of major liquidity pools and yield profits comparable to MEV. Most prior AMM models utilised the Black-Scholes (BS) stochastic differential equation (SDE) - i.e., geometric Brownian motion - and assumed continuous price trajectories where asset prices move in small increments only.We argue that BS underestimates arbitrage profits by ignoring price jumps, which are precisely the points at which arbitrage opportunities tend to arise. To address this gap, we present an extended discrete-time AMM model in which the price process is the sum of a diffusive component and stochastic jumps that can have arbitrary noise distributions. Although mathematically more involved this framework allows us to employ a general discrete-time SDE and compute the stationary probability distribution via function iteration with geometric convergence. We further prove that the resulting mispricing process is an ergodic Markov chain. We implement our model in C++, collect spot prices and AMM exchange data from the Ethereum blockchain and fit the model parameters to the observed prices. The estimates derived from our model closely match empirical observations and provide a natural theoretical explanation for several fundamental questions in the blockchain ecosystem.

翻译：以太坊生态系统的核心问题在于：最大可提取价值（MEV）收入源自何处，以及其在多大程度上源于对不知情用户的损害。若MEV源自中心化交易所与去中心化交易所（CEX-DEX）之间的套利，这尚可接受。然而，理论模型严重低估了此类套利的规模，尽管实证研究强调了其重要性——但此类研究仍属保守估计，且受制于诸多存在争议的启发式假设。通过重新审视理论模型，我们发现CEX-DEX套利所需交易量需达到主要流动性池总活动量级，其产生的利润也与MEV相当。先前多数自动做市商（AMM）模型采用布莱克-舒尔斯（BS）随机微分方程（SDE）——即几何布朗运动——并假设资产价格仅以微小增量变动的连续价格轨迹。我们指出，BS模型忽略了价格跳跃（恰是套利机会易现的关键节点），从而低估了套利利润。为弥补这一缺陷，我们提出一种扩展的离散时间AMM模型，其中价格过程由扩散分量与可具有任意噪声分布的随机跳跃之和构成。尽管数学上更复杂，该框架使我们能够采用一般化的离散时间SDE，并通过具有几何收敛性的函数迭代计算平稳概率分布。我们进一步证明，由此产生的错误定价过程是一个遍历马尔可夫链。我们用C++实现该模型，收集以太坊区块链上的现货价格与AMM交易所数据，并将模型参数拟合至观测价格。从我们模型推导出的估计值与实证观测高度吻合，并为区块链生态系统中的若干基本问题提供了自然的理论解释。