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

Project: Research project

Project Details


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 the term structure of interest rates break down when the short term interest rate is at the zero lower bound (ZLB).
This project proposes a novel class of interest rate models with the sticky zero lower bound based on the mathematics of diffusions with sticky boundaries. This class of diffusions 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 proposes to develop analytical and computational tools to work with these stochastic processes, including computational algorithms specifically tailored for this class of models, and apply them to develop and empirically test concrete interest rate model specifications.

Intellectual Merit:
The intellectual merit of this proposal is in the development of a novel class of interest rate models based on diffusions with sticky boundaries, and in the associated computational methods to solve stochastic differential equations with sticky boundaries and partial differential equations with Wentzell boundary conditions.
This proposal combines theoretical development of interest rate models based on diffusions with sticky boundaries, high performance implementation on parallel architecture of computational algorithms to solve these models numerically, and statistical estimation on empirical interest rate data.

Broader Impacts:
The broader impact is in applications in the financial industry to the pricing and hedging of interest rate sensitive financial instruments, managing interest rate risk, and fixed income portfolio construction, as well as in central banking to aid in conducting monetary policy, as well as in training of doctoral students in financial mathematics and engineering.
This project, if funded, will train Ph.D. students in the financial engineering concentration at Northwestern (established by the PI). Former Ph.D. students in the FE concentration are now faculty members (UIUC, UT Austin, UW Seattle, CUHK) and financial engineers in the financial industry.
Effective start/end date9/1/158/31/18


  • National Science Foundation (DMS-1514698)


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