Modeling interest rate dynamics: an infinite-dimensional approach

TL;DR

This paper introduces an infinite-dimensional stochastic model for interest rate term structures, capturing key features like mean reversion and maturity correlations, with practical calibration methods.

Contribution

It develops a novel infinite-dimensional framework for modeling interest rate dynamics, including stochastic PDEs, and connects model parameters to observable data.

Findings

Captures essential features of yield curve dynamics

Provides a parsimonious description of interest rate fluctuations

Offers a natural interpretation of parameters in empirical terms

Abstract

We present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of the short rate, the long rate and the fluctuations of the curve around its average shape. This fluctuation is then described as a solution of a stochastic evolution equation in an infinite dimensional space. In the case where deformations are local in maturity, this equation reduces to a stochastic PDE, of which we give the simplest example. We discuss the properties of the solutions and show that they capture in a parsimonious manner the essential features of yield curve dynamics: imperfect correlation between maturities, mean reversion of interest rates and the structure of principal components of term structure deformations. Finally, we discuss calibration issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.