State space decomposition and classification of term structure shapes in the two-factor Vasicek model

Paper: arXiv 2303.13966

Authors: Martin Keller-Ressel, Felix Sachse

Abstract

Using the concept of envelopes we show how to divide the state space $\RR^2$ of the two-factor Vasicek model into regions of identical term-structure shape. We develop a formula for determining the shapes utilizing winding numbers and give a nearly complete classification of the parameter space regarding the occurring shapes.

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical and mathematical analysis of state space decomposition in the two-factor Vasicek model using envelopes and winding numbers. However, it is purely theoretical and completely lacks empirical backtesting, market data validation, or calibration to real yield curves.

Research Flowchart

  flowchart TD
    A[Goal: Classify term structure shapes in 2-factor Vasicek model] --> B[Input: Model parameters & state space R²]
    B --> C[Compute envelopes of yield curve functions]
    C --> D[Apply winding numbers to determine curve shape topology]
    D --> E[Decompose state space R² into distinct shape regions]
    E --> F[Outcome: Complete classification map of parameter space]