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.