Pricing and clearing combinatorial markets with singleton and swap orders

Johannes C. Müller (), Sebastian Pokutta, Alexander Martin, Susanne Pape, Andrea Peter and Thomas Winter
Additional contact information
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

Mathematical Methods of Operations Research, 2017, vol. 85, issue 2, No 1, 155-177

Abstract: 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.

Keywords: Equilibrium problems; Hierarchical objectives; Linear programming; Network flows; Combinatorial auctions; Futures exchanges; 90C33; 90C29; 90C05; 90C35; 91B26 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s00186-016-0555-z

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