Financial options are contracts that specify the right to buy or sell an underlying asset at a strike price by an expiration date. Standard exchanges offer options of predetermined strike values and trade options of different strikes independently, even for those written on the same underlying asset. Such independent market design can introduce arbitrage opportunities and lead to the thin market problem. The paper first proposes a mechanism that consolidates and matches orders on standard options related to the same underlying asset, while providing agents the flexibility to specify any custom strike value. The mechanism generalizes the classic double auction, runs in time polynomial to the number of orders, and poses no risk to the exchange, regardless of the value of the underlying asset at expiration. Empirical analysis on real-market options data shows that the mechanism can find new matches for options of different strike prices and reduce bid-ask spreads. Extending standard options written on a single asset, we propose and define a new derivative instrument -- combinatorial financial options that offer contract holders the right to buy or sell any linear combination of multiple underlying assets. We generalize our single-asset mechanism to match options written on different combinations of assets, and prove that optimal clearing of combinatorial financial options is coNP-hard. To facilitate market operations, we propose an algorithm that finds the exact optimal match through iterative constraint generation, and evaluate its performance on synthetically generated combinatorial options markets of different scales. As option prices reveal the market's collective belief of an underlying asset's future value, a combinatorial options market enables the expression of aggregate belief about future correlations among assets.

中文翻译：

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设计组合金融期权市场

金融期权是指定在到期日之前以执行价格买卖标的资产的权利的合约。标准交易所独立提供预定行使价的期权和不同行使价的交易期权，即使是写在同一基础资产上的期权。这种独立的市场设计可以引入套利机会并导致市场稀缺问题。该论文首先提出了一种机制，可以整合和匹配与同一基础资产相关的标准期权的订单，同时为代理提供指定任何自定义执行价值的灵活性。该机制概括了经典的双重拍卖，根据订单数量按时间多项式运行，并且无论标的资产在到期时的价值如何，都不会给交易所带来风险。对实物市场期权数据的实证分析表明，该机制可以为不同执行价格的期权找到新的匹配，并降低买卖价差。扩展基于单一资产的标准期权，我们提出并定义了一种新的衍生工具——组合金融期权，为合约持有人提供购买或出售多种基础资产的任何线性组合的权利。我们将我们的单一资产机制推广到匹配写在不同资产组合上的期权，并证明组合金融期权的最佳清算是 coNP-hard。为了促进市场操作，我们提出了一种算法，通过迭代约束生成找到精确的最佳匹配，并评估其在不同规模的综合生成组合期权市场上的表现。