On the deterministic-shift extended CIR model in a negative interest rate framework
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.
Cite
@article{arxiv.2203.07458,
title = {On the deterministic-shift extended CIR model in a negative interest rate framework},
author = {Marco Di Francesco and Kevin Kamm},
journal= {arXiv preprint arXiv:2203.07458},
year = {2022}
}