Shape of term structures compatible with flexible choice of diffusion

2025/09/22 by Andreas Celary, Celary, Andreas, Paul Krühner +1
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #Mathematical Biology Tumor Growth #Mathematical Finance (q-fin.MF) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2509.17875

openalex publication_date 2025/09/22 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/31

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.

Citations

• Statistically consistent term structures have affine geometry
• Discount Models
• Existence of affine realizations for stochastic partial differential equations driven by Lévy processes
• A new perspective on the fundamental theorem of asset pricing for large\n financial markets
• Discrete Time Term Structure Theory and Consistent Recalibration Models
• Some refinements of existence results for SPDEs driven by Wiener processes and Poisson random measures
• Invariant manifolds with boundary for jump-diffusions
• Finite dimensional Realizations of Stochastic Equations

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