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

Marco Di Francesco and Kevin Kamm
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Marco Di Francesco: UnipolSai Assicurazioni, Via Stalingrado 45, 40128 Bologna, Italy
Kevin Kamm: Dipartimento di Matematica, Università di Bologna, 40126 Bologna, Italy

IJFS, 2022, vol. 10, issue 2, 1-26

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.

Keywords: CIR model; negative interest rates; calibration; Riccati equations; swaptions; Bermudan swaptions (search for similar items in EconPapers)
JEL-codes: F2 F3 F41 F42 G1 G2 G3 (search for similar items in EconPapers)
Date: 2022
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