Term Structure of Interest Rates. Emergence of Power Laws and Scaling Laws

TL;DR

This paper applies Padé Approximants to US interest rate variation data, revealing new power laws and scaling laws across maturities, especially for one-year rates, indicating complex underlying dynamics.

Contribution

It introduces the use of Padé Approximants to identify power and scaling laws in interest rate variations across different maturities and initial rates.

Findings

Power laws and scaling laws emerge for interest rate variations.

Critical forms and exponents are identified for one-year maturity.

Results suggest complex, scale-invariant behavior in interest rate dynamics.

Abstract

The technique of Pad\'e Approximants, introduced in a previous work, is applied to extended recent data on the distribution of variations of interest rates compiled by the Federal Reserve System in the US. It is shown that new power laws and new scaling laws emerge for any maturity not only as a function of the Lag but also as a function of the average inital rate. This is especially true for the one year maturity where critical forms and critical exponents are obtained. This suggests future work in the direction of constructing a theory of variations of interest rates at a more ``microscopic'' level.}