AI 中文总结
研究二元利率奇异衍生品定价，利用约束薛定谔最优传输问题的对偶拉格朗日函数构建建模框架，能在三个关联市场保持一致，可计算无套利边界，通过数值示例展示适用性，为复杂利率衍生品定价提供有力工具。
AI 中文摘要
我们开发了一个用于对二元利率奇异衍生品定价的建模框架，该框架在三个相互关联的市场中保持一致性：CMS利差期权以及定义该利差的两个基础CMS期权市场。我们的方法还能够根据利差期权和基础CMS期权市场中可观测的市场价格计算奇异衍生品的无套利边界。该方法依赖于求解约束薛定谔最优传输问题的对偶拉格朗日函数，我们通过具体数值示例展示了框架的实际适用性，这些示例说明了定价方法和无套利边界的计算。该方法为定价复杂利率衍生品提供了一个强大工具，同时确保与流动性市场工具的一致性。
英文摘要
We develop a modeling framework for pricing bivariate interest rate exotic derivatives that maintains consistency across three interconnected markets: CMS spread options and the two underlying CMS option markets that define the spread. Our approach also enables the computation of no-arbitrage bounds for exotic derivatives given observable market prices in the spread option and underlying CMS option markets. The method relies on solving the dual Lagrangian of a constrained version of the Shrödinger optimal transport problem and we demonstrate the practical applicability of our framework through concrete numerical examples that illustrate both the pricing methodology and the computation of no-arbitrage bounds. The approach offers a robust tool for pricing complex interest rate derivatives while ensuring consistency with liquid market instruments.
