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

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  • 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.

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  • 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.
    • Handle: RePEc:arx:papers:2303.13966
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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.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. 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.
    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    5. 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.
    6. 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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