Paying for speed, hedging the wait: Execution risk and optimal priority fees in arbitrage between centralised and decentralised crypto exchanges

Technical Summary: Execution Risk and Optimal Priority Fees in CEX–DEX Arbitrage

Problem Statement
Arbitrage between Centralised Exchanges (CEX) and Decentralised Exchanges (DEX) involves a fundamental asymmetry in execution speed. While the CEX leg of an arbitrage trade is filled instantaneously, the DEX leg is subject to a random delay while waiting in the public mempool for block inclusion. During this stochastic delay, asset prices on both venues fluctuate, introducing execution risk. Under the Ethereum EIP-1559 fee market, traders can reduce this expected delay by paying a higher priority fee, effectively purchasing speed. However, this creates a decision problem: how much should an arbitrageur pay for speed, and how much of the exposure during the wait should be hedged using CEX futures? The paper addresses the joint optimization of the priority fee and the hedge size to maximize risk-adjusted returns, noting that existing literature often treats these decisions separately or ignores the specific execution risk inherent to DEX mempool delays.

Methodology
The paper formulates the arbitrageur's problem as a stochastic control task with two control variables: the priority fee ($g$) and the futures hedge size ($h$).

1. Model Structure:

   • Delay Modeling: The waiting time ($\tau$) is modeled as the first jump of a counting process with an intensity $\lambda(g)$ that increases with the priority fee. The paper assumes an exponential distribution for $\tau$, where the mean delay is $1/\lambda(g)$.
   • Price Dynamics: Prices on the CEX, DEX, and the hedging futures contract follow correlated geometric Brownian motions.
   • Profit Function: The profit of a single arbitrage cycle includes the initial spread, minus the cost of slippage, the gas fee, and the price impact during the delay.
   • Objective: The author employs a mean–variance objective function ($J = E[\Pi] - \frac{\gamma}{2}Var[\Pi]$), where $\gamma$ represents risk aversion. This is justified as a two-moment approximation for small risks and short horizons.

2. Analytical Approach:

   • Static Solution: The problem is first solved in a static, single-cycle setting. The author derives closed-form solutions for the optimal hedge and the optimal priority fee.
   • Dynamic Solution: A dynamic version is formulated using a Hamilton–Jacobi–Bellman (HJB) equation with controlled execution intensity. This dynamic model is solved numerically to verify that the static closed-form rules serve as a valid first-order approximation.
   • Assumptions: Key assumptions include the conditional independence of the delay from future price increments and a reduced-form model for slippage where expected slippage is inversely proportional to the inclusion intensity.

3. Data and Calibration:

   • The model is calibrated using public data from Binance (CEX), Uniswap v3 (DEX), and the Ethereum blockchain (gas data).
   • The study covers the period from January 2021 to May 2026, with specific focus on the "calm" market of 2026 and nine historical periods of varying network congestion (e.g., NFT boom, Terra collapse, FTX collapse).
   • Parameters such as the elasticity of inclusion intensity with respect to fees ($\beta$) and slippage coefficients are estimated via regression on historical data.

Key Contributions
The paper makes three primary contributions to the literature on DeFi and execution risk:

1. Joint Decision Framework: It formulates CEX–DEX arbitrage as a unified risk-management problem where the trader simultaneously chooses the priority fee and the hedge. It demonstrates that these decisions separate: the optimal hedge depends on the correlation between assets, while the optimal fee depends on the unhedged portion of the risk.
2. Explicit Pricing of Speed: The paper provides an explicit formula for the optimal priority fee, showing it is a function of trade size, risk aversion, volatility, and the unhedgeable share of risk. It confirms via the HJB equation that this static formula is a robust approximation of the dynamic policy.
3. Empirical Validation: The study calibrates the model on real-world data and tests it across different market regimes. It moves beyond theoretical equilibrium models to provide tractable decision rules for execution under delay.

Results

• Hedging Efficacy: The optimal minimum-variance hedge removes approximately 93.9% of the price variance during the wait. Crucially, the optimal hedge ratio is independent of the priority fee.
• Optimal Fee Behavior:
  • In calm markets (e.g., 2026), the optimal fee is typically at the lower bound (the minimum required for inclusion). In these conditions, the optimized rule performs identically to a simple fixed-fee rule because the cost of waiting is low and speed is cheap.
  • In congested markets, the optimized rule significantly outperforms fixed-fee strategies. Across nine historical regimes, the optimized rule achieved a higher Sharpe ratio in eight cases.
• Quantitative Gains: On a dataset of 182,562 on-chain arbitrage swaps, the optimized closed-form rule earned USD 2.59 more per trade than a fixed-fee rule.
• Regime Dependence: The value of optimizing the fee is positively correlated with network congestion. In highly congested periods (e.g., December 2021), the fixed-fee rule resulted in a negative Sharpe ratio, while the optimized rule remained positive.

Significance and Claims
The paper claims to fill a gap in the literature by treating CEX–DEX arbitrage not just as a price-alignment mechanism, but as a risk-management problem involving a public execution queue. Its significance lies in providing a tractable model for decision-making under execution delay, rather than an equilibrium model of the fee market.

The author modestly claims that their results offer practical guidance for arbitrageurs: "Hedge the wait first, and pay for speed only when the remaining risk is large." This implies that for small positions or in calm networks, complex fee optimization is unnecessary, but for large positions or during network stress, dynamic fee adjustment is critical for profitability. The paper also highlights that the cost of speed on a blockchain is a fundamental component of the cost of maintaining price alignment between on-chain and off-chain markets, a cost ultimately borne by liquidity providers and users.

The study acknowledges limitations, including the assumption of a price-taking agent (ignoring strategic MEV competition), the use of a reduced-form inclusion model, and the focus on a single trading pair (ETH/USDC). It does not claim to model the full equilibrium of the fee market or the strategic behavior of block builders.