Pricing and clearing combinatorial markets with singleton and swap orders: Efficient algorithms for the futures opening auction problem

TL;DR

This paper introduces a polynomial-time algorithm for efficiently clearing and pricing combinatorial markets with singleton and swap orders, specifically applied to the futures opening auction, reducing operational risks and potential arbitrage.

Contribution

It presents a novel polynomial-time algorithm for market-clearing and pricing in combinatorial markets with singleton and swap orders, applied to futures auctions.

Findings

Algorithm guarantees consistent prices in futures opening auctions.

Empirical tests show the algorithm's suitability for production environments.

Addresses operational risks and arbitrage in futures markets.

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.