具有单一订单和互换订单的组合市场的定价和清算：期货开盘拍卖问题的有效算法
Pricing and clearing combinatorial markets with singleton and swap orders: Efficient algorithms for the futures opening auction problem
摘要：
在这篇文章中，我们考虑的组合市场的估值只为单件和对购买/出售订单交换两个项目在相同的数量。我们提供了一个算法，允许多项式时间的市场出清和定价。结果的背景下，我们的主要应用：期货开盘拍卖问题。期货合约是降低市场风险和交易对手信用风险的重要工具。在期货市场上，这些合约可以在不同的到期日和基础上进行交易。一种常见的对冲策略是将头寸滚动到下一个到期日，但这种策略会带来重大的操作风险。为了解决这一风险，交易所开始提供所谓的期货合约组合，允许交易员交换两个到期日不同的期货合约，或者交换两个基础不同的期货合约。理论上，在这两种情况下，价格都是两份期货合约的差价。然而，特别是在开盘拍卖中，由于次优清算，经常发生价格效率低下的情况，从而导致潜在的套利机会。我们提出了一个最小成本流制定的期货开盘拍卖问题，保证一致的价格。其核心思想是将订单建模为网络中的弧，在两个分层目标的帮助下执行均衡条件，并将这些目标组合成一个加权目标，同时保留双重最优解的价格信息。由此产生的最优化问题可以在多项式时间内求解，并且计算测试建立了适合于生产环境的经验性能。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
