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Term structure shapes in the Hull-White model with Svensson-parameterized initial yield curves

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  • Felix Sachse

Abstract

We examine the shapes attainable by the forward and yield curve in the Hull-White model with Svensson-parameterized initial yield curves. For Nelson-Siegel-parameterized initial yield curves, we provide a complete classification of all attainable shapes and partition the parameter space and the state space according to these shapes. Our analysis relies on the theory of Tchebycheff systems and the envelope method. For Bliss- and Svensson-parameterized initial yield curves, we derive lower and upper bounds on the number of attainable local extrema. We examine the asymptotic behavior of the model and demonstrate that the yield curve attains only the shapes normal, inverse and humped with positive probability as $t\rightarrow\infty.$

Suggested Citation

  • Felix Sachse, 2026. "Term structure shapes in the Hull-White model with Svensson-parameterized initial yield curves," Papers 2608.12016, arXiv.org.
    • Handle: RePEc:arx:papers:2608.12016
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    References listed on IDEAS

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    2. Martin Keller-Ressel, 2018. "Correction to: Yield curve shapes and the asymptotic short rate distribution in affine one-factor models," Finance and Stochastics, Springer, vol. 22(2), pages 503-510, April.
    3. Martin Keller‐Ressel & Felix Sachse, 2026. "Term Structure Shapes and Their Consistent Dynamics in the Svensson Family," Mathematical Finance, Wiley Blackwell, vol. 36(1), pages 140-155, January.
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    8. Martin Keller-Ressel & Felix Sachse, 2023. "State space decomposition and classification of term structure shapes in the two-factor Vasicek model," Papers 2303.13966, arXiv.org.
    9. Martin Keller-Ressel, 2017. "Erratum to: `Yield curve shapes and the asymptotic short rate distribution in affine one-factor models'," Papers 1711.00737, arXiv.org, revised Feb 2018.
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