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.