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

TL;DR

This paper introduces a new exogenous extension of the CIR model using a deterministic shift to effectively model negative interest rates while maintaining analytical tractability and fitting observed market data.

Contribution

It proposes a novel deterministic-shift extended CIR model based on the difference of two CIR processes, enabling negative rates and fast calibration.

Findings

Model accurately fits the observed term-structure.

Produces Bermudan swaption prices close to Bloomberg's model.

Finds CMS rates very close to Bloomberg's rates.

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.