How to handle negative interest rates in a CIR framework

TL;DR

This paper introduces a novel, analytically tractable model for negative interest rates based on the difference of two CIR processes, avoiding shifts and fitting market data effectively.

Contribution

It proposes a simple, new CIR-based model that handles negative rates without shifts and can be calibrated analytically to market curves.

Findings

The model accurately reproduces market term structures.

Simulation results match the skewness and fat tails of the CIR model.

Zero coupon prices and swaptions are consistent with market data.

Abstract

In this paper, we propose a new model to address the problem of negative interest rates that preserves the analytical tractability of the original Cox-Ingersoll-Ross (CIR) model without introducing a shift to the market interest rates, because it is defined as the difference of two independent CIR processes. The strength of our model lies within the fact that it is very simple and can be calibrated to the market zero yield curve using an analytical formula. We run several numerical experiments at two different dates, once with a partially sub-zero interest rate and once with a fully negative interest rate. In both cases, we obtain good results in the sense that the model reproduces the market term structures very well. We then simulate the model using the Euler-Maruyama scheme and examine the mean, variance and distribution of the model. The latter agrees with the skewness and fat tail seen in the original CIR model. In addition, we compare the model's zero coupon prices with market prices at different future points in time. Finally, we test the market consistency of the model by evaluating swaptions with different tenors and maturities.