Where Does MEV Really Come From? Revisiting CEXDEX Arbitrage on Ethereum

1. Problem Statement

The paper addresses a fundamental discrepancy in the Ethereum ecosystem regarding the source and scale of Maximal Extractable Value (MEV).

• The Discrepancy: Empirical studies suggest that CEX–DEX arbitrage (arbitrage between Centralized and Decentralized Exchanges) accounts for a massive portion of MEV revenue and trading volume, far exceeding the volume of "benign" atomic arbitrage or sandwich attacks. However, existing theoretical models significantly underestimate these figures.
• The Root Cause: Prior theoretical models rely on the Black–Scholes (BS) framework, which assumes asset prices follow a continuous path (Geometric Brownian Motion) with small, incremental changes.
• The Flaw: The authors argue that the BS model fails because it ignores price jumps. In reality, arbitrage opportunities often arise precisely when prices jump discontinuously (e.g., sudden large movements in ETH price). By assuming continuous trajectories, BS models miss the primary mechanism driving arbitrage volume and profit.

2. Methodology

The authors propose a new mathematical framework to model the mispricing process between CEX and DEX prices.

A. Extended Discrete-Time Stochastic Model

Instead of continuous-time SDEs, the authors use a discrete-time approach (aligned with Ethereum's block time) that incorporates both diffusion and jumps:

• Price Dynamics: The log-price process $X_n$ is defined recursively:
  $$X_{n+1} - X_n = \mu(X_n) + \sigma(X_n)\epsilon_{n+1} + Z_{n+1}U_{n+1}$$
  • Diffusive Component: $\mu$ (drift) and $\sigma$ (volatility) with noise $\epsilon$.
  • Jump Component: $Z_{n+1}$ is a Bernoulli variable indicating a jump, and $U_{n+1}$ is the jump amplitude.
  • Generality: The noise distribution $\epsilon$ is not restricted to Gaussian; it can have arbitrary distributions (including heavy tails). This model subsumes Black–Scholes, Merton Jump Diffusion, and Ornstein–Uhlenbeck processes as special cases.

B. Arbitrage Mechanism

The model simulates a "myopic" arbitrageur who acts when the logarithmic mispricing ($\tilde{X}_n$) exceeds a threshold defined by the AMM fee ($\gamma$).

• If $\tilde{X}_n > \gamma_+$, the arbitrageur trades to reset the price to $\gamma_+$.
• If $\tilde{X}_n < -\gamma_-$, the price is reset to $-\gamma_-$.
• The system is modeled as a Markov Chain where the state is the mispricing level.

C. Theoretical Analysis

• Stationary Probability Distribution (SPD): The authors prove that under mild assumptions (constant drift/volatility and bounded noise density), the mispricing process is an ergodic Markov chain.
• Convergence: They demonstrate that the stationary distribution can be computed via function iteration with geometric convergence. This allows for the calculation of the invariant density $f^*(x)$ without needing closed-form solutions.
• Derivations: Using the SPD, they derive closed-form expressions for:
  • Expected arbitrage trading volume.
  • Expected arbitrage profit.
  • Long-term frequency of trades.

D. Empirical Implementation

• Data Collection: The authors collected on-chain data from a major Uniswap V2 ETH–USDT pool (Sept 13–29, 2025) and off-chain spot prices from major CEXs (Binance, KuCoin, Gate.io) at 1-second resolution.
• Parameter Fitting: They fitted the model parameters ($\mu, \sigma, q, \mu_J, \sigma_J$) to the observed data. Crucially, they used a threshold $\tau$ to distinguish between "diffusive" movements and "jumps."
• Simulation: A C++ numerical integrator was used to compute the SPD via function iteration (100 steps) and calculate expected volumes and profits.

3. Key Contributions

1. Theoretical Correction: The paper proves that the Black–Scholes assumption of continuous paths is insufficient for modeling AMM arbitrage. It introduces a jump-diffusion discrete-time model that accurately captures the "spiky" nature of crypto price movements.
2. Mathematical Rigor: The authors provide a rigorous proof that the mispricing process is an ergodic Markov chain and that its stationary distribution can be computed efficiently via iteration.
3. Reconciliation of Theory and Practice: The new model produces estimates that align closely with empirical observations, resolving the long-standing gap between theoretical predictions (low volume) and empirical reality (high volume).
4. Open Source Tooling: The authors released a C++ implementation to allow for reproducibility and further exploration of stochastic AMM models.

4. Key Results

• Volume Discrepancy Resolved:
  • Old Models (BS): Predicted daily arbitrage volume of ~$208k for the tested pool.
  • Empirical Data: Observed volume was ~$3.3M (all swaps) with CEX-DEX arbitrage heuristics identifying ~$970k.
  • New Model: Predicted volume of ~$1.88M, which is roughly 9x higher than the BS model and closely matches the empirical upper bounds.
• Profitability: The model estimates arbitrage profits of ~$1,454/day, which is comparable to the total MEV extracted from the pool, suggesting the arbitrage market is highly competitive and saturated.
• Role of Jumps: The fitted parameters showed a jump probability ($q$) of ~4.5% per second, with jump sizes having heavy tails. The model confirmed that price jumps are the primary driver of arbitrage volume, not the continuous diffusion assumed by previous models.
• Noise Traders: The analysis suggests that "noise traders" (traders not reacting to price gaps) contribute a minor fraction of the total volume compared to arbitrage-driven trades.
• Block Time: The authors conclude that reducing block times (e.g., faster blocks) is unlikely to reduce MEV significantly because the opportunities arise from price jumps, which occur regardless of block frequency.

5. Significance

• MEV Origins: The paper provides a natural theoretical explanation that a significant portion of MEV revenue stems from CEX–DEX arbitrage, which is a necessary mechanism for AMMs to track external market prices, rather than just "predatory" attacks like sandwiching.
• Market Design: It challenges the assumption that faster block times will eliminate MEV. Since jumps are the driver, the speed of price discovery (CEX vs. DEX) matters more than block propagation speed.
• Empirical Heuristics: The study suggests that current empirical methods for identifying arbitrage (which rely on strict heuristics like "first swap in a block") may be overly restrictive, missing a large volume of hidden arbitrage activity that the new model predicts.
• Financial Modeling: It establishes a more robust framework for modeling crypto-asset prices, moving beyond the Gaussian/Black–Scholes paradigm to include jumps and non-Gaussian noise, which is critical for accurate risk and profit assessment in DeFi.

In summary, the paper demonstrates that ignoring price jumps leads to a massive underestimation of MEV and arbitrage volume. By incorporating jumps into a discrete-time stochastic model, the authors successfully bridge the gap between theoretical finance and the empirical reality of the Ethereum ecosystem.