Paper: arXiv 2410.08808

Authors: Martin Keller-Ressel, Felix Sachse

Abstract

We examine the shapes attainable by the forward- and yield-curve in the widely-used Svensson family, including the Nelson-Siegel and Bliss subfamilies. We provide a complete classification of all attainable shapes and partition the parameter space of each family according to these shapes. Building upon these results, we then examine the consistent dynamic evolution of the Svensson family under absence of arbitrage. Our analysis shows that consistent dynamics further restrict the set of attainable shapes, and we demonstrate that certain complex shapes can no longer appear after a deterministic time horizon. Moreover a single shape (either inverse of normal curves) must dominate in the long-run.

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 rigorous mathematical classification of the attainable term structure shapes within the widely used Svensson family and analyzes their consistent dynamic evolution under no-arbitrage constraints. The theoretical results are strong and cleanly derived, complemented by empirical validation using two decades of ECB yield curve data.

Research Flowchart

  flowchart TD
    A[Goal: Classify shapes & analyze no-arbitrage dynamics in Svensson family] --> B[Input: Svensson, Nelson-Siegel, & Bliss yield/forward curve models]
    B --> C[Method 1: Static Parameter Space Partitioning]
    B --> D[Method 2: Dynamic Arbitrage-Free Consistency Analysis]
    C --> E[Outcome 1: Complete classification of all attainable curve shapes]
    D --> F[Outcome 2: No-arbitrage restricts shapes; complex shapes disappear over time]
    E & F --> G[Final Finding: Long-run curves must be dominated by a single shape]

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  10. State Space Decomposition And Classification Of Term Structure Shapes In The Two-Factor Vasicek Model — → 2303.13966
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1 of 22 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.