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The classification of term structure shapes in the two-factor Vasicek model -- a total positivity approach

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  • Martin Keller-Ressel

Abstract

We provide a full classification of all attainable term structure shapes in the two-factor Vasicek model of interest rates. In particular, we show that the shapes normal, inverse, humped, dipped and hump-dip are always attainable. In certain parameter regimes up to four additional shapes can be produced. Our results apply to both forward and yield curves and show that the correlation and the difference in mean-reversion speeds of the two factor processes play a key role in determining the scope of attainable shapes. The key mathematical tool is the theory of total positivity, pioneered by Samuel Karlin and others in the 1950ies.

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  • 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.
    • Handle: RePEc:arx:papers:1908.04667
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    References listed on IDEAS

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    1. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
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    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    6. 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.
    7. 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.
    8. 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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    Cited by:

    1. Martin Keller-Ressel & Felix Sachse, 2024. "Term structure shapes and their consistent dynamics in the Svensson family," Papers 2410.08808, arXiv.org.

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