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Pricing and clearing combinatorial markets with singleton and swap orders

Author

Listed:
  • Johannes C. Müller

    (FAU Erlangen-Nürnberg)

  • Sebastian Pokutta

    (ISyE, Georgia Institute of Technology)

  • Alexander Martin

    (FAU Erlangen-Nürnberg)

  • Susanne Pape

    (FAU Erlangen-Nürnberg)

  • Andrea Peter

    (FAU Erlangen-Nürnberg)

  • Thomas Winter

    (Eurex Frankfurt AG)

Abstract

In this article we consider combinatorial markets with valuations only for singletons and pairs of buy/sell-orders for swapping two items in equal quantity. We provide an algorithm that permits polynomial time market-clearing and -pricing. The results are presented in the context of our main application: the futures opening auction problem. Futures contracts are an important tool to mitigate market risk and counterparty credit risk. In futures markets these contracts can be traded with varying expiration dates and underlyings. A common hedging strategy is to roll positions forward into the next expiration date, however this strategy comes with significant operational risk. To address this risk, exchanges started to offer so-called futures contract combinations, which allow the traders for swapping two futures contracts with different expiration dates or for swapping two futures contracts with different underlyings. In theory, the price is in both cases the difference of the two involved futures contracts. However, in particular in the opening auctions price inefficiencies often occur due to suboptimal clearing, leading to potential arbitrage opportunities. We present a minimum cost flow formulation of the futures opening auction problem that guarantees consistent prices. The core ideas are to model orders as arcs in a network, to enforce the equilibrium conditions with the help of two hierarchical objectives, and to combine these objectives into a single weighted objective while preserving the price information of dual optimal solutions. The resulting optimization problem can be solved in polynomial time and computational tests establish an empirical performance suitable for production environments.

Suggested Citation

  • Johannes C. Müller & Sebastian Pokutta & Alexander Martin & Susanne Pape & Andrea Peter & Thomas Winter, 2017. "Pricing and clearing combinatorial markets with singleton and swap orders," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 85(2), pages 155-177, April.
  • Handle: RePEc:spr:mathme:v:85:y:2017:i:2:d:10.1007_s00186-016-0555-z
    DOI: 10.1007/s00186-016-0555-z
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    References listed on IDEAS

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    1. Babaioff, Moshe & Feldman, Michal & Nisan, Noam & Winter, Eyal, 2012. "Combinatorial agency," Journal of Economic Theory, Elsevier, vol. 147(3), pages 999-1034.
    2. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    3. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.
    4. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    5. Sven de Vries & Rakesh V. Vohra, 2003. "Combinatorial Auctions: A Survey," INFORMS Journal on Computing, INFORMS, vol. 15(3), pages 284-309, August.
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    Cited by:

    1. Fred Glover & Gary Kochenberger & Moses Ma & Yu Du, 2022. "Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange," Annals of Operations Research, Springer, vol. 314(1), pages 185-212, July.
    2. Fred Glover & Gary Kochenberger & Moses Ma & Yu Du, 2020. "Quantum Bridge Analytics II: QUBO-Plus, network optimization and combinatorial chaining for asset exchange," 4OR, Springer, vol. 18(4), pages 387-417, December.

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