finance   Cox Ingersoll Ross Model

## Definition of Cox Ingersoll Ross Model

Cox–Ingersoll–Ross model is one of the important models in short rate model; it is implemented to describe the evolution of interest rates. This model can be interpreted by mathematical formula, which model the movement of interest rate driven by a sole source of market risk.

• In CIR model’s calculations that a square root diffusion model stands for short-term interest rates with a mean reversion. The usage of the CIR model is widely implemented on the valuation of interest rate derivatives.
• The advantage of the CIR model is interest counted as positive after the calculations, (≥ 0), with probability 1. This is considered as the biggest convenience of CIR model.
• This model was first introduced by John C. Cox, Jonathan E. Ingersoll and Stephen A. Ross in 1985, and this model is the outcome of Vasicek Interest Rate model.

## Books on Cox Ingersoll Ross Model

### Book 1:

Statistics of Financial Markets: An Introduction By Jürgen Franke, Wolfgang Karl Härdle, Christian Matthias Hafner (published by Springer Science & Business Media, 2010)

### Book 2:

Financial Derivatives in Theory and Practice By Philip Hunt, Joanne Kennedy (Published by John Wiley and Sons, 2004)

## How Cox Ingersoll Ross Model works?

Here are a few practical examples, with which the idea of Cox–Ingersoll–Ross model will be defined,

• Cox–Ingersoll–Ross model is administered to evaluate the chronological development of bonds return depending on the time of maturity, the model start with identifying the one or more factors to assist the structure to assist to determine term structure, in this model the through specification of the dynamic model with specific expectation hypothesis, we can obtain a explicit solution for the returns.
• As a practical example, suppose the price of the zero coupon bond with the nominal value of 1 EUR is interpreted as PT(t) at time t, at the maturity date T, the security has no dividend payments that entitled to pay 1 EUR, YT(t) tell the value of the log return of the zero coupon bond. W is assumed as continuous compounding hold, the yield of maturity is referred as YT(t),

As the CIR factor is widely used to determine the short rates, the CIR model specifies the dynamic of the short rate as the continuous stochastic process,

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