# Cox-Ingersoll-Ross Model – Definition

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### Cox-Ingersoll-Ross Model Definition

The Cox-Ingersoll-Ross model (CIR) is regarded as an interest rate model. It is a mathematical formula based on a stochastic differential equation in which one or more of the terms is a stochastic process, giving a solution known as a stochastic process. The Cox-Ingersoll-Ross model (CIR) is applicable in finance, it is a model that describes the evolution of interest rates.

The CIR model is driven by market risk element, it is useful in modelling interest rate movements in the market. The model determines how interest rate evolve due to current volatility, mean rates and their spread. CIR uses mean reversion towards a long-term normal interest rate level.

### A Little More on What is the Cox-Ingersoll-Ross Model

The Cox-Ingersoll-Ross (CIR) model was derived from the Vasicek Interest Rate model,which was also a mathematical formula used in the evaluation of interest rate movements. However, the Vasicek model does not include a square root component and it sometimes model negative interest rates.

In the valuation process of interest rate derivatives, the Cox-Ingersoll-Ross model is often used. CIR explicitly describes the evolution of interest rates. John C. Cox, Jonathan E Ingersoll and Stephen A. Ross created the Cox-Ingersoll-Ross (CIR) model in 1985. CIR has an advantage over the Vasicek model because it does not allow for or model negative interest rates.

### Academic Research on Cox, Ingersoll, Ross Option-Pricing Model

Pricing interest rate options in a two-factor CoxIngersollRoss model of the term structure, Chen, R. R., & Scott, L. (1992). The review of financial studies, 5(4), 613-636.

The empirical implications of the Cox, Ingersoll, Ross theory of the term structure of interest rates, Brown, S. J., & Dybvig, P. H. (1986). The Journal of Finance, 41(3), 617-630.

Computing the constant elasticity of variance option pricing formula, Schroder, M. (1989). the Journal of Finance, 44(1), 211-219.

Interest rate option pricing with Poisson‐Gaussian forward rate curve processes, Shirakawa, H. (1991). Mathematical Finance, 1(4), 77-94.

Pricing stock options in a jump‐diffusion model with stochastic volatility and interest rates: Applications of Fourier inversion methods, Scott, L. O. (1997). Mathematical Finance, 7(4), 413-426.

Option Pricing When Jump Risk Is Systematic1, Ahn, C. M. (1992). Mathematical Finance, 2(4), 299-308.

Cross-sectional versus time series estimation of term structure models: Empirical results for the Dutch bond market, de Munnik, J. F., & Schotman, P. C. (1994). Journal of Banking & Finance, 18(5), 997-1025.

An empirical comparison of alternative models of the short‐term interest rate, Chan, K. C., Karolyi, G. A., Longstaff, F. A., & Sanders, A. B. (1992). The journal of finance, 47(3), 1209-1227.

Multi-factor term structure models, Duffie, D., & Kan, R. (1994). Phil. Trans. R. Soc. Lond. A, 347(1684), 577-586.

The pricing of stock index options in a general equilibrium model, Bailey, W., & Stulz, R. M. (1989). Journal of Financial and Quantitative Analysis, 24(1), 1-12.

Stochastic duration and fast coupon bond option pricing in multi-factor models, Munk, C. (1999). Review of Derivatives Research, 3(2), 157-181.

Evaluating the noncentral chi-square distribution for the CoxIngersollRoss process, Dyrting, S. (2004). Computational economics, 24(1), 35-50.