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On the Deterministic-Shift Extended CIR Model in a Negative Interest Rate Framework

Author

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  • Marco Di Francesco

    (UnipolSai Assicurazioni, Via Stalingrado 45, 40128 Bologna, Italy
    These authors contributed equally to this work.)

  • Kevin Kamm

    (Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy
    These authors contributed equally to this work.)

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 between 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.

Suggested Citation

  • Marco Di Francesco & Kevin Kamm, 2022. "On the Deterministic-Shift Extended CIR Model in a Negative Interest Rate Framework," IJFS, MDPI, vol. 10(2), pages 1-26, May.
    • Handle: RePEc:gam:jijfss:v:10:y:2022:i:2:p:38-:d:820074
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    References listed on IDEAS

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    2. Ho, Thomas S Y & Lee, Sang-bin, 1986. "Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-1029, December.
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    5. Cornelis W Oosterlee & Lech A Grzelak, 2019. "Mathematical Modeling and Computation in Finance:With Exercises and Python and MATLAB Computer Codes," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number q0236, February.
    6. 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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