Paper: arXiv 2509.17875

Authors: Andreas Celary, Paul Krühner

Abstract

We identify all smooth manifolds of curves for Heath-Jarrow-Morton models that are consistent with any tangential diffusion coefficient. In fact, we show that these manifolds cannot be affine but must be of linear-rational type.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 1.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a rigorous theoretical analysis of Heath-Jarrow-Morton (HJM) interest rate models, establishing that manifolds consistent with arbitrary tangential diffusions must be of linear-rational type rather than affine. It features heavy functional analysis and differential geometry applied to term structure theory, but is purely mathematical with no empirical backtesting or data validation.

Research Flowchart

  flowchart TD
    A[Research Goal: Identify HJM smooth manifolds<br/>compatible with flexible diffusion] --> B[Input: Heath-Jarrow-Morton HJM framework<br/>& tangential diffusion coefficients]
    B --> C[Method: Geometric & Functional Analysis<br/>of finite-dimensional curve manifolds]
    C --> D[Process: Solve consistency conditions<br/>for arbitrary diffusion choices]
    D --> E[Outcome 1: Prove manifolds<br/>cannot be affine]
    D --> F[Outcome 2: Characterize valid structures<br/>as linear-rational manifolds]

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2 of 94 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.