Explaining the Forward Interest Rate Term Structure

TL;DR

This paper introduces a new interpretation of the forward interest rate term structure, revealing a square-root law relationship with spot volatility and an anticipated trend mechanism, challenging existing models.

Contribution

It provides empirical evidence for a novel interpretation of the FRC, linking it to a square-root law and past spot trends, and critiques the adequacy of the Gaussian HJM model.

Findings

FRC follows a square-root law related to spot volatility

Strong correlation between FRC and past spot trend

Gaussian HJM model fails to capture observed features

Abstract

We present compelling empirical evidence for a new interpretation of the Forward Rate Curve (FRC) term structure. We find that the average FRC follows a square-root law, with a prefactor related to the spot volatility, suggesting a Value-at-Risk like pricing. We find a striking correlation between the instantaneous FRC and the past spot trend over a certain time horizon. This confirms the idea of an anticipated trend mechanism proposed earlier and provides a natural explanation for the observed shape of the FRC volatility. We find that the one-factor Gaussian Heath-Jarrow-Morton model calibrated to the empirical volatility function fails to adequately describe these features.