Interest Rate Modeling at the Zero Lower Bound: Applications of Diffusions with Sticky Boundaries

自2008年全球金融危机以来，由于各国央行对金融危机和随后的经济衰退采取的货币政策反应，美国、欧元区和日本的短期利率一直接近于零。 当短期利率处于零下限（ZLB）时，传统的利率数学模型就会崩溃。 该项目基于具有粘性边界的扩散过程的数学，开发并研究了一类新颖的零下限利率数学模型。 该项目的预期影响是在金融行业中对利率敏感的金融工具的定价和对冲、管理利率风险、固定收益投资组合构建、在中央银行中帮助实施货币政策以及金融数学和工程博士生的培训。 具有粘性边界的扩散类别非常适合 ZLB 建模的挑战，因为它自然地提供了具有两种不同经济体制的模型 - 远离边界的过程和边界上的过程。 该项目开发分析和计算工具来处理具有粘性边界的扩散，包括专门为此类随机过程定制的计算方法，并将它们应用于开发和实证测试利率模型。 该项目的智力优势在于开发了一类基于粘性边界扩散的新型利率模型，以及求解具有粘性边界的随机微分方程和具有 Wentzell 边界条件的偏微分方程的相关分析和计算方法。 研究生也包括在该项目中。

Short-term interest rates in the U.S., the Euro zone, and Japan have been near zero since the global financial crisis of 2008, due to the monetary policy responses by the central banks to the financial crisis and the recession that followed. Conventional mathematical models of interest rates break down when the short term interest rate is at the zero lower bound (ZLB). This project develops and investigates a novel class of mathematical models of interest rates with the zero lower bound based on the mathematics of diffusion processes with sticky boundaries. The anticipated impact of the project is in applications in the financial industry to the pricing and hedging of interest-rate-sensitive financial instruments, to managing interest rate risk, to fixed income portfolio construction, and in central banking to aid in conducting monetary policy, as well as in training of doctoral students in financial mathematics and engineering. The class of diffusions with sticky boundaries is well suited to the challenge of modeling the ZLB, as it naturally supplies a model with two distinct economic regimes -- the process away from the boundary and the process on the boundary. This project develops analytical and computational tools to work with diffusions with sticky boundaries, including computational methods specifically tailored for this class of stochastic processes, and applies them to develop and empirically test interest rate models. The intellectual merit of this project is in the development of a novel class of interest rate models based on diffusions with sticky boundaries, and in the associated analytical and computational methods to solve stochastic differential equations with sticky boundaries and partial differential equations with Wentzell boundary conditions. Graduate students are included in the project.