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Term structure shapes and their consistent dynamics in the Svensson family

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  • 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.

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  • Martin Keller-Ressel & Felix Sachse, 2024. "Term structure shapes and their consistent dynamics in the Svensson family," Papers 2410.08808, arXiv.org.
    • Handle: RePEc:arx:papers:2410.08808
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    References listed on IDEAS

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    1. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    2. Martin Keller-Ressel, 2021. "The Classification Of Term Structure Shapes In The Two-Factor Vasicek Model — A Total Positivity Approach," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(05), pages 1-27, August.
    3. Robert R. Bliss, 1996. "Testing term structure estimation methods," FRB Atlanta Working Paper 96-12, Federal Reserve Bank of Atlanta.
    4. 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.
    5. Martin Keller-Ressel & Thomas Steiner, 2008. "Yield curve shapes and the asymptotic short rate distribution in affine one-factor models," Finance and Stochastics, Springer, vol. 12(2), pages 149-172, April.
    6. 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.
    7. Nelson, Charles R & Siegel, Andrew F, 1987. "Parsimonious Modeling of Yield Curves," The Journal of Business, University of Chicago Press, vol. 60(4), pages 473-489, October.
    8. Martin Keller-Ressel, 2019. "The classification of term structure shapes in the two-factor Vasicek model -- a total positivity approach," Papers 1908.04667, arXiv.org, revised Jun 2021.
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