Paper: arXiv 2506.03342

Authors: Andreas Celary, Paul Krühner, Zehra Eksi

Abstract

We consider the theory of bond discounts, defined as the difference between the terminal payoff of the contract and its current price. Working in the setting of finite-dimensional realizations in the HJM framework, under suitable notions of no-arbitrage, the admissible discount curves take the form of polynomial, exponential functions. We introduce reproducing kernels that are admissible under no-arbitrage as a tractable regression basis for the estimation problem in calibrating the model to market data. We provide a thorough numerical analysis using real-world treasury data.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a strong theoretical contribution by integrating reproducing kernel Hilbert space (RKHS) methods with the HJM discount curve framework under strict NAFLVR no-arbitrage conditions. It combines rigorous functional analysis and measure transformations with an empirical calibration on US Treasury bond data.

Research Flowchart

  flowchart TD
    A[Goal: Model & calibrate discount curves using RKHS under No-Arbitrage] --> B[Theory: Formulate finite-dimensional HJM framework with polynomial/exponential basis]
    B --> C[Methodology: Construct admissible Reproducing Kernels satisfying No-Arbitrage]
    D[Input: Real-World Treasury Market Data] --> E[Computation: Perform RKHS regression for model calibration]
    C --> E
    E --> F[Outcomes: Tractable estimation & validation via numerical analysis]

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2 of 96 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.