Non-Atomic Arbitrage Overview

Updated 11 October 2025

Non-atomic arbitrage is characterized by pricing inconsistencies emerging from global market structures rather than isolated, atomic events.
Mathematical tools like topological criteria and functional analysis reveal arbitrage opportunities by capturing joint asset inconsistencies and ensuring pathwise continuity.
Practically, non-atomic arbitrage manifests in decentralized finance and derivatives markets where multi-step trades and execution risks define unique risk-reward profiles.

Non-atomic arbitrage encompasses a broad class of arbitrage phenomena in financial markets where opportunities arise or are precluded not because of discrete, isolated (atomic) price inconsistencies, but as a consequence of global, topological, or collective properties of the market structure, information flows, or temporal sequencing of trades. The concept appears in both classical deterministic trajectory-based frameworks, advanced derivatives and volatility modeling, decentralized finance (DeFi), prediction markets, and models involving insider or informational structures. This entry synthesizes the technical manifestations, mathematical tools, operational settings, and economic implications of non-atomic arbitrage, referencing developments across mathematical finance and decentralized systems.

1. Non-Atomic Arbitrage: Definitions and Frameworks

Non-atomic arbitrage is characterized by arbitrage opportunities that:

Cannot be isolated to atomistic (measure-zero or scenario-specific) events,
Emerge or become apparent only on the level of collections of securities, combinations of market conditions, or over sequences of actions that are not synchronously bundled,
Require analysis beyond “atomic” arbitrage, which is typically evinced by strict local violations (e.g., in a single derivative's price or snapshot of the market).

Classical, deterministic frameworks ("non-probabilistic arbitrage") define arbitrage in terms of pathwise properties over trajectory spaces endowed with topological structures (Alvarez et al., 2011). A portfolio exhibits non-atomic arbitrage if it produces nonnegative terminal payoffs on all price trajectories and a strictly positive payoff on some non-negligible (open, topologically meaningful) neighborhood in the trajectory space. Admissible portfolios are required to be continuous (or semicontinuous) with respect to the trajectory topology, ruling out arbitrage strategies that exploit only isolated, atomistic paths.

In multi-asset or derivative settings, non-atomic arbitrage may arise when the vector of traded prices is globally inconsistent—i.e., there is no joint market structure (e.g., an equivalent martingale measure or consistent copula) supporting all observed marginal prices, even though each security's individual price lies within its own no-arbitrage interval (Papapantoleon et al., 2020). This type of opportunity can only be detected when considering the joint ensemble of instruments.

In prediction markets, non-atomic arbitrage appears when combinations of bets or positions across outcomes or logically related markets create riskless profit opportunities, even if no single transaction reveals an arbitrage at the atomic level (Saguillo et al., 5 Aug 2025).

Unlike atomic arbitrage (e.g., classical call-put violations or on-chain atomic swap loops), non-atomic arbitrage often requires multi-step or asynchronous (non-atomic) trade execution, information aggregation, or pathwise continuity properties to be uncovered or exploited.

2. Mathematical Structures and Topological Criteria

Non-atomic arbitrage is fundamentally informed by topological and functional analytic considerations:

Trajectory Space and Continuity: In deterministic markets, arbitrage is defined relative to a trajectory space $J$ (e.g., space of continuous or càdlàg paths under the uniform or Skorohod topology) and a class of admissible portfolios $A$ , typically satisfying self-financing and bounded-below properties. The admissibility criterion is “ $V$ -continuity”: the terminal portfolio value $x \mapsto V_\phi(T, x)$ must be continuous or semicontinuous. The absence of arbitrage is defined so that no $V$ -continuous strategy can achieve nonnegative terminal value everywhere and strictly positive value on a non-negligible neighborhood (Alvarez et al., 2011).
Transfer to Probabilistic Models: The connection to classical arbitrage is established via support properties and continuity: if the stochastic price process has “small ball support” (positive measure for any open set in the trajectory topology), then pathwise (non-atomic) arbitrage conditions imply probabilistic arbitrage considerations, and vice versa (Theorems 1 and 2 in (Alvarez et al., 2011)).
Copula Consistency and Multi-Asset Markets: In derivative markets, arbitrage-free pricing requires that a set of traded prices corresponds to an admissible copula (joining given marginals into a joint distribution). Existence of such a copula is nontrivial when multiple derivatives are traded: each individual price may be arbitrage-free in isolation, but the collection may be jointly inconsistent—exhibiting non-atomic arbitrage (Papapantoleon et al., 2020). The condition is rigorously formulated as the non-emptiness of the intersection of sets defined by improved Fréchet–Hoeffding bounds (pointwise, functional constraints on the copula).
Functional Portfolio Generation: In equity markets, the only portfolios that guarantee pathwise (non-atomic, or “pseudo-”) relative arbitrage under diversity and volatility are “functionally generated portfolios,” characterized by concave generating functions and the property of multiplicative cyclical monotonicity (Pal et al., 2014). Such portfolios exploit volatility in the market weights in an aggregated (non-atomic) manner, not through isolated price jumps or discrete event arbitrage.

3. Practical Manifestations: Decentralized Finance and Execution Risks

Non-atomic arbitrage is pervasive in decentralized finance (DeFi), having distinct operational signatures:

Atomic vs. Non-Atomic Execution: In DEX environments, classic “atomic” arbitrage is executed as a single transaction (e.g., a cyclic swap on a single chain or AMM), guaranteeing that all legs succeed together or fail together (Wang et al., 2021). Non-atomic arbitrage, by contrast, involves asynchronous or multi-step trades: e.g., buying on-chain and then selling off-chain (or vice versa), or crossing venues/chains in a way that exposes the arbitrageur to price drift risk (Heimbach et al., 3 Jan 2024, Gogol et al., 4 Jun 2024, Silva et al., 15 Oct 2024).
Statistical Prevalence: Empirical work shows that a substantial fraction (over 25%) of DEX trading volume on major Ethereum-based platforms arises from non-atomic arbitrage, primarily conducted by a handful of vertically integrated searcher-builder teams ( $\sim$ 80% of volume controlled by only 11 entities, totaling over $132$ billion (Heimbach et al., 3 Jan 2024)).
Execution Challenges and Centralization Risks: Non-atomic arbitrage opportunities carry execution risk due to price drift between trade legs, latency, and potential front-running, making them accessible mainly to privileged actors with high integration and rapid execution capabilities (Silva et al., 15 Oct 2024). The centralization of such searchers has been linked to increased concentration in block production and MEV extraction, particularly under consensus changes (e.g., Ethereum's PBS).
Cross-Rollup and L2 Phenomena: With the rise of L2 rollups, non-atomic arbitrage extends across rollups and between DEX-CEX venues, with misalignments persisting for multiple blocks (typically $10$–$20$ on rollups), resulting in regular, measurable opportunities (0.03–0.25% of trading volume on major rollups) (Gogol et al., 4 Jun 2024). The inherent risk and decay over time necessitate modified metrics for MEV and loss-versus-rebalancing calculations.
Adversarial Manipulation: The emergence of bribery-enabled delayed block production in Ethereum 2.0 (BriDe Arbitrager) expands the non-atomic arbitrage surface by granting malicious proposers additional time to sequence transactions and create artificial arbitrage cycles through strategic transaction ordering and bribery (Yang et al., 11 Jul 2024). This exploits protocol-level “delays” to increase arbitrage profitability and further accentuates centralization tendencies.
Algorithmic Innovations: Closed-form, parallelizable solutions for arbitrage in $N$ -token AMMs (Willetts et al., 9 Feb 2024) provide computationally efficient alternatives to convex solvers, enabling real-time, large-scale non-atomic arbitrage detection and execution.

4. Market Design, Derivatives, and Option Pricing

Non-atomic arbitrage critically informs option pricing, volatility modeling, and market design:

Volatility Surface Construction: The SVI parameterization for implied volatility surfaces requires explicit constraints (on calendar spreads and butterfly shapes) to exclude static (non-atomic) arbitrage—i.e., no portfolio can “exploit” random convexity violations to synthesize riskless profit with atomless portfolios (Gatheral et al., 2012). Calibration methods enforce these constraints via closed-form conditions in the parameter space.
Discrete Models and Minmax Approaches: Trajectory-based discrete models relax no-arbitrage to “0-neutrality,” whereby arbitrage may exist in specific (atomic) scenarios, but the global, worst-case (min-max) profit can be driven arbitrarily close to zero (Ferrando et al., 2014). This setting permits rich pricing intervals and martingale-like properties without strict exclusion of atomic arbitrage paths.
Prediction Markets and Combinatorial Opportunities: In combinatorial prediction markets, non-atomic arbitrage can be identified when combined outcome prices (e.g., across logically linked markets) do not sum to 1, enabling multi-market, multi-step arbitrage strategies—though at the cost of significant execution risk due to the non-atomicity of trades (Saguillo et al., 5 Aug 2025). Detection requires advanced heuristics, dependency analysis, and LLM-assisted relationship extraction.

5. Informational, Model-Theoretic, and Regulatory Perspectives

The informational architecture of a market shapes the prevalence and detectability of non-atomic arbitrage:

Stability Under Information Enlargement: In discrete time, the preservation of non-arbitrage in the presence of extra (e.g., insider) information depends on regularity conditions (e.g., the behavior of Azéma supermartingales) (Choulli et al., 2014). If these conditions fail, non-atomic arbitrage can be constructed by exploiting temporal or structural discontinuities.
Insider Models and Bounded Risk: With insiders possessing non-atomic (continuous) information, market viability (e.g., well-posedness of utility maximization) can be maintained so long as unbounded profit with bounded risk is excluded (NUPBR holds), even though arbitrage of the “first kind” may be feasible (Chau et al., 2016). Regulatory frameworks and market monitoring must address these subtler forms of arbitrage, which escape detection by classical atomic checks.

6. Open Questions and Implications for Protocol Design

Open challenges and future directions for research and system design include:

Measurement and Mitigation: How to robustly measure (and possibly mitigate) non-atomic arbitrage in highly composable, cross-venue systems given the prevalence of execution risk, latency, and protocol-level manipulations (e.g., delayed block production).
Optimal Sequencing and Shared Sequencer Architectures: Atomic execution mechanisms (e.g., shared sequencers for rollups) may unintentionally reduce arbitrage profitability and even be suboptimal for market efficiency when non-atomic strategies are permitted (Silva et al., 15 Oct 2024). Designing protocol features that balance the need for fair ordering, MEV minimization, and flexibility remains a challenge.
Market Efficiency and Welfare: The economic impact of non-atomic arbitrage—both in extracting economic surplus (as with $40$ million USD extracted in prediction market settings (Saguillo et al., 5 Aug 2025)) and in affecting the security, inclusiveness, and fairness of markets—demands further paper, especially as financial systems increasingly rely on on-chain and cross-chain composability.
Theoretical Characterization: Filling the gap between topological, functional analytic, and probabilistic criteria for non-atomic arbitrage, and clarifying the trade-offs in market diversity, portfolio generation, and model robustness (Herczegh et al., 2013, Pal et al., 2014, Fernholz et al., 2016).

7. Summary Table: Non-Atomic Arbitrage Across Domains

Domain	Core Mechanism	Key Reference
NP Trajectory Frameworks	V-continuous portfolios, topology	(Alvarez et al., 2011)
Multi-Asset Derivatives	Joint copula inconsistency	(Papapantoleon et al., 2020)
DeFi: Ethereum DEX–CEX Arbitrage	Off-chain/on-chain price gaps	(Heimbach et al., 3 Jan 2024)
DeFi: Cross-Rollup/Layer-2	Multi-block, cross-domain trades	(Gogol et al., 4 Jun 2024)
Bribery and Block Delay Attacks	Transaction ordering via consensus	(Yang et al., 11 Jul 2024)
Volatility Surface Construction	Static (non-atomic) smiles, SVI	(Gatheral et al., 2012)
Prediction/Combinatorial Markets	Execution risk, pricing sum mismatch	(Saguillo et al., 5 Aug 2025)
Insider/Informational Models	Non-atomic extra information	(Chau et al., 2016)
Atomicity in Shared Sequencers	Flexibility loss vs MEV optimization	(Silva et al., 15 Oct 2024)

References

(Alvarez et al., 2011) Arbitrage and Hedging in a non probabilistic framework
(Gatheral et al., 2012) Arbitrage-free SVI volatility surfaces
(Herczegh et al., 2013) Diversity and no arbitrage
(Pal et al., 2014) The geometry of relative arbitrage
(Choulli et al., 2014) Non-arbitrage for Informational Discrete Time Market Models
(Ferrando et al., 2014) Discrete, Non Probabilistic Market Models. Arbitrage and Pricing Intervals
(Lukkarinen et al., 2016) Arbitrage without borrowing or short selling?
(Chau et al., 2016) Arbitrage and utility maximization in market models with an insider
(Fernholz et al., 2016) Volatility and Arbitrage
(Naiman et al., 2017) Arbitrage and Geometry
(Papapantoleon et al., 2020) Detection of arbitrage opportunities in multi-asset derivatives markets
(Wang et al., 2021) Cyclic Arbitrage in Decentralized Exchanges
(Heimbach et al., 3 Jan 2024) Non-Atomic Arbitrage in Decentralized Finance
(Willetts et al., 9 Feb 2024) Closed-form solutions for generic N-token AMM arbitrage
(Gogol et al., 4 Jun 2024) Cross-Rollup MEV: Non-Atomic Arbitrage Across L2 Blockchains
(Yang et al., 11 Jul 2024) BriDe Arbitrager: Enhancing Arbitrage in Ethereum 2.0 via Bribery-enabled Delayed Block Production
(Silva et al., 15 Oct 2024) Atomic Execution is Not Enough for Arbitrage Profit Extraction in Shared Sequencers
(Saguillo et al., 5 Aug 2025) Unravelling the Probabilistic Forest: Arbitrage in Prediction Markets