Unified Field Theory and Boundary Laws of Interest Rates: An Instantaneous Rolling Forward Rate Approach

Unified Boundary Field Theory of Interest Rates

Abstract

Interest-rate modelling has developed through several powerful but partially distinct traditions. Each of these traditions has been extraordinarily productive, yet a conceptual separation remains. In many models, the dynamic consistency of the term structure is handled in one part of the framework, while the shape of the curve, the maturity profile of volatility, and the effect of monetary policy are introduced elsewhere through additional parametrisation.

Humped volatility structures, curve-shape restrictions, maturity loadings, and policy effects are often specified because they are useful or empirically plausible, rather than derived from a common structural mechanism.

The purpose of this monograph is to investigate whether more of this structure can be generated from fewer principles, while preserving a clear account of the modelling cost.

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An Axiomatically Consistent Single-Factor Term Structure Model with Admissible Humped Volatility

Abstract

We develop an axiomatic framework for the dynamics of the instantaneous rolling forward rate and the associated term structure of interest rates.

These conditions admit the IRFR to a Pearson-type diffusion with affine drift and quadratic volatility.

1. Core Research Paper

2. Presentation & Tutorial Slide Deck

3. Video Presentation & Tutorials

Monetary Policy as a Boundary Condition in the IRFR Framework

Abstract

Monetary policy operates at the short end of the interest-rate curve, directly influencing the overnight rate while leaving the remainder of the forward curve to market determination.

This paper argues that the appropriate mathematical representation of this asymmetry is through boundary conditions imposed at zero maturity.

1. Core Research Paper

Stochastic Long-Maturity Boundary States

Abstract

This paper extends the IRFR boundary-field framework from the short end of the maturity manifold to the stochastic long end. Earlier work introduced the IRFR field representation and showed that short-end boundary closures generate the linear-exponential repeated-root hump τe−a2τ.

The present paper distinguishes the equilibrium long-run anchor x∞ from the realised long-boundary state Xt, derives a minimal multiplicative long-boundary law, and embeds the long boundary in a completed three-loading maturity representation.

1. Core Research Paper

Empirical Evidence for a Unified Boundary-Field Theory of Interest Rates

Abstract

This paper provides an empirical test of the Robin short-rate boundary-coordinate layer in Unified Boundary Field Theory (UBFT). The central claim is not merely that Treasury yield curves are low-dimensional. Rather, the paper asks whether a single short-rate boundary geometry can organise several empirical objects that are usually modelled separately: yieldcurve shape, maturity-dependent volatility, local boundary anchoring, covariance geometry, and phase-state behaviour.

Those papers present a theory in which a central claim is that a single maturity-space boundary geometry can organise multiple observables extracted from the same interest-rate dataset: yield-curve shape, the spatial decay parameter a2, interest-rate volatility, covariance rank, and market-price-of-risk structure. This paper provides the empirical test for that claim.

1. Core Research Paper

2. Core Research Paper Supplement

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