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On the deterministic-shift extended CIR model in a negative interest rate framework

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  • Marco Di Francesco
  • Kevin Kamm

Abstract

In this paper, we propose a new exogenous model to address the problem of negative interest rates that preserves the analytical tractability of the original Cox-Ingersoll-Ross (CIR) model with a perfect fit to the observed term-structure. We use the difference of two independent CIR processes and apply the deterministic-shift extension technique. To allow for a fast calibration to the market swaption surface, we apply the Gram-Charlier expansion to calculate the swaption prices in our model. We run several numerical tests to demonstrate the strengths of this model by using Monte-Carlo techniques. In particular, the model produces close Bermudan swaption prices compared to Bloomberg's Hull-White one-factor model. Moreover, it finds constant maturity swap (CMS) rates very close to Bloomberg's CMS rates.

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  • Marco Di Francesco & Kevin Kamm, 2022. "On the deterministic-shift extended CIR model in a negative interest rate framework," Papers 2203.07458, arXiv.org.
    • Handle: RePEc:arx:papers:2203.07458
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    References listed on IDEAS

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    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. 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.
    3. Keiichi Tanaka & Takeshi Yamada & Toshiaki Watanabe, 2010. "Applications of Gram-Charlier expansion and bond moments for pricing of interest rates and credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 645-662.
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