Double Auctions: Formalization and Automated Checkers (2410.18751v1)

Abstract: Double auctions are widely used in financial markets, such as those for stocks, derivatives, currencies, and commodities, to match demand and supply. Once all buyers and sellers have placed their trade requests, the exchange determines how these requests are to be matched. The two most common objectives for determining the matching are maximizing trade volume at a uniform price and maximizing trade volume through dynamic pricing. Prior research has primarily focused on single-quantity trade requests. In this work, we extend the framework to handle multiple-quantity trade requests and present fully formalized matching algorithms for double auctions, along with their correctness proofs. We establish new uniqueness theorems, enabling automatic detection of violations in exchange systems by comparing their output to that of a verified program. All proofs are formalized in the Coq Proof Assistant, and we extract verified OCaml and Haskell programs that could serve as a resource for exchanges and market regulators. We demonstrate the practical applicability of our work by running the verified program on real market data from an exchange to automatically check for violations in the exchange algorithm.

• The paper presents a formalized framework for double auctions using the Coq Proof Assistant to extract verified matching algorithms in OCaml and Haskell.
• It extends methodologies to handle multi-quantity trades while ensuring regulatory compliance through uniform, fair, and maximum matching outcomes.
• The work offers a practical tool for detecting discrepancies in exchange algorithms, thereby enhancing trust and robustness in financial market systems.

Formalization and Verification of Double Auction Mechanisms

The paper "Double Auctions: Formalization and Automated Checkers" by Garg et al. addresses the intricate problem of double auctions in financial markets. It tackles the challenges of verifying and ensuring compliance with regulatory guidelines, which mandate fairness, uniform prices, and rationality in auction outcomes. The paper extends existing frameworks to handle multiple-quantity trade requests, formalizes matching algorithms, and provides correctness proofs through a systematic formalization using the Coq Proof Assistant. This work also extracts verified programs in OCaml and Haskell, offering a valuable resource for exchanges and regulators.

Framework and Definitions

The authors provide a comprehensive introduction to double auctions, discussing their application across a variety of financial products like stocks, commodities, and currencies. The formal framework for analyzing outcomes of double auctions centers around maximizing trade volumes under different conditions: uniform pricing or dynamic pricing. The novelty lies in expanding the focus from single-quantity trades to multiple-quantity trades, requiring a more robust mathematical framework and formal verification.

Key definitions include:

• Uniform Matching: All transactions closed at the same price.
• Fair Matching: More competitive bids or asks get prioritized.
• Maximum Matching: Maximizes trade volume irrespective of uniformity.
• Optimal-Uniform Matching: Maximizes trade volume while maintaining uniformity.

The authors develop formalized algorithms for each class of these matchings, extracting them into executable code verified to meet specified conditions.

Formal Verification

A primary challenge tackled by the authors is formalizing the correctness of matching algorithms through Coq Proof Assistant. They present uniqueness theorems which facilitate automatic detection of potential violations of auction mechanisms. The Coq formalization encompasses approximately 9000 lines, with proofs structured around key properties:

• Fairness: The Fair algorithm ensures that any matching can be converted into one that is both fair and indistinguishable in volume from the original.
• Uniform and Maximum Matchings: Procedures UM and MM are derived to provide guarantees on uniformity and trade volume maximization, respectively, supported by formal proofs.

Numerical Results and Theoretical Implications

The paper does not rest solely on theoretical advancements; it demonstrates practical applicability by testing the extracted programs on real market data. Differences in outputs between exchange results and their verified program can indicate discrepancies in the exchange’s matching algorithm. The unique approach allows for nuanced detection of potential regulatory violations or operational anomalies, emphasizing the importance of verified algorithms to ensure system integrity in financial markets.

Speculation on AI Developments

The introduction of formal verification and automated checks in double auctions opens new avenues for integrating AI into financial systems. While AI can optimize trading strategies and automate processes, incorporation of formal verification can mitigate risks of erroneous decisions or violations, ensuring compliance and robustness. Future developments may further automate these processes, potentially incorporating AI-driven adaptive auction strategies that meet regulatory standards in real-time.

Conclusion

The paper by Garg et al. is a substantial contribution to the field of economic mechanisms, enhancing the reliability and integrity of financial exchanges through formalization and automated verification. The extracted verified programs could set new standards for regulatory compliance, ensuring fairness and efficiency in highly dynamic and complex market environments. As financial systems integrate more sophisticated AI components, these foundational verification frameworks will likely play a crucial role in maintaining system stability and trust.