Phenomenology of the Term Structure of Interest Rates with Pade Approximants

TL;DR

This paper explores a phenomenological approach to modeling the term structure of interest rates using Padé Approximants, demonstrating their effectiveness in fitting empirical data with minimal parameters.

Contribution

It introduces the use of Padé Approximants for interest rate modeling and shows they can accurately reproduce empirical interest rate variation densities with only two parameters.

Findings

Padé Approximants fit interest rate variation data well

Two parameters suffice to model the distributions

Parameters relate to moments and are functions of lag and maturity

Abstract

The classical approach in finance attempts to model the term structure of interest rates using specified stochastic processes and the no arbitrage argument. Up to now, no universally accepted theory has been obtained for the description of experimental data. We have chosen a more phenomenological approach. It is based on results obtained some twenty years ago by physicists, results which show that Pad\'e Approximants are very suitable for approximating large classes of functions in a very precise and coherent way. In this paper, we have chosen to compare Pad\'e Approximants with very low indices with the experimental densities of interest rates variations. We have shown that the data published by the Federal Reserve System in the United States are very well reproduced with two parameters only. These parameters are rather simple functions of the lag and of the maturity and are directly related to the moments of the distributions.