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 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.

Rating Triggers for Collateral-Inclusive XVA via Machine Learning and SDEs on Lie Groups

“…This would allow us to extract information about the market volatilities similar to a calibration to zero-coupon prices in an interest rate framework (cf. [5] and [6]).…”