Term Structure Shapes in the Hull–White Model with Svensson–Parameterized Initial Yield Curves

Battle Count: 80

The paper provides fundamental theoretical insights into which yield curve shapes are attainable in the Hull-White model, which is widely used for interest rate derivative pricing and risk management. Understanding shape constraints is relevant for: (1) validating model outputs against observed market shapes, (2) detecting model misspecification, (3) informing trading strategies based on yield curve shape transitions, (4) risk management of fixed income portfolios, and (5) calibration of term structure models. However, the paper is purely theoretical and does not provide direct trading signals or implementable algorithms.

The paper involves highly advanced mathematical machinery including Tchebycheff systems, ECT-systems, Wronskian determinants, envelope theory, tracking functions, Lambert W-functions, and winding number calculations. The case-by-case analysis spans multiple parameter regimes with complex boundary conditions. Implementing the full classification and segmentation would require sophisticated symbolic and numerical computation. The theoretical framework is deeply rooted in approximation theory and differential geometry.

The paper provides complete mathematical proofs, explicit formulas for tracking functions, envelopes, and segmentation boundaries. All parameter regimes are fully characterized with case-by-case analysis. The theoretical framework is self-contained with detailed appendices on Tchebycheff systems. However, no numerical code or computational implementation is provided. The paper is based on two chapters of the author's doctoral thesis [Sac26].