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.
