# Cox Ingersoll Ross Model

Cox Ingersoll Ross Model Overview:
Cox-Ingersoll-Ross Model was formulated in 1985. The people responsible for formulating the Cox-Ingersoll-Ross Model were John C. Cox, Stephen A. Ross and Jonathan E. Ingersoll. The Cox Ingersoll Ross Model is a supplement of the Vasicek Model.
Cox Ingersoll Ross Model Description
The Cox Ingersoll Ross Model deals basically with the development of rates of interest. The Cox Ingersoll Ross Model is a “one factor model”. The Cox Ingersoll Ross Model could also be called a Short rate model.

The main reason behind this is that the Cox Ingersoll Ross Model considers only market risk to be the principal reason behind the changes in interest rates.

Use of Cox Ingersoll Ross Model
The Cox Ingersoll Ross Model could be used to determine the value of interest rate derivatives.
Equational Representation of Cox Ingersoll Ross Model

Following is the numerical presentation of Cox Ingersoll Ross Model:

drt = a(b – rt) dt + σ√rtdWt

In this model Wt is a Wiener process. It models the factor of random market risk
Cox Ingersoll Ross Model Drift Factor

The drift factor of the Cox Ingersoll Ross Model is a(b – rt). It is similar to the drift factor of the Vasicek Model. It is used to make sure that the average reversion of rate of interest is in the direction of b, which is value for long run.

This average reversion of interest rate needs to have an adjustment speed. This adjustment speed needs to be governed by a, which is supposed to be a purely positive standard.

Cox Ingersoll Ross Model Standard Deviation Factor

The standard deviation factor of the Cox Ingersoll Ross Model is σ√rt. It makes sure that the interest rate does not become negative. 