## What Is the Cox-Ingersoll-Ross Model (CIR)?

The Cox-Ingersoll-Ross model (CIR) is a mathematical formula used to model interest rate movements and is driven by a sole source of market risk. It is used as a method to forecast interest rates and is based on a stochastic differential equation.

The Cox-Ingersoll-Ross (CIR) model was developed in 1985 by John C. Cox, Jonathan E. Ingersoll and Stephen A. Ross as an offshoot of the Vasicek Interest Rate model.

## Understanding the CIR Model

The Cox-Ingersoll-Ross model determines interest rate movements as a product of current volatility, the mean rate and spreads. Then, it introduces a market risk element. The square root element does not allow for negative rates and the model assumes mean reversion towards a long-term normal interest rate level. The Cox-Ingersoll-Ross model is often used in the valuation of interest rate derivatives.

### Key Takeaways

• The CIR is used to forecast interest rates.
• The CIR is a one-factor equilibrium model that uses a square-root diffusion process to ensure that the calculated interest rates are always non-negative.

## The Difference Between the CIR and the Vasicek Interest Rate Model

Like the Cox-Ingersoll-Ross model, the Vasicek model is also a one-factor modeling method. However, the Vasicek model allows for negative interest rates as it does not include a square root component.

It was long thought that the inability of the model to produce negative rates was a big advantage of the Cox-Ingersoll-Ross model over the Vasicek model, but in recent years as many European central banks have introduced negative rates this stance has been rethought.