On Term Structure of Yield Rates. 2. The Cox – Ingersoll – Ross Model

Tomsk State University Journal of Control and Computer Science. 2012. No. 2(19). pp. 102-111.

7 Pages Posted: 20 Jun 2017

Date Written: January 20, 2012

Abstract

Historically, the first popular model of the dynamics of the interest rate is the Vasiček model proposed in 1977. It was considered in the preceding article. In this model, the interest rate has a normal distribution, which is obviously economically untenable, because in terms of the interest rate can not take negative values. At the same time, this model has been used by many for the reason that in many cases the ratio between the average and variance of real rates is such that the probability of their negative values appears very small. At the same time, the analysis of Vasicek's model and the prices of assets based on it is very simple, since it leads to linear problems. Later in 1985, Cox, Ingersoll and Ross proposed another model, also called a "square root model," under which the interest rate assumes only non-negative values and has a gamma distribution. Analysis of interest rates and asset prices based on this model also allows for analytical results, but they are significantly more difficult, since they suggest solving non-linear problems. The possibility of obtaining analytical results is the main advantage of affine models. Analytical results are important, because otherwise yields should be calculated either by Monte Carlo methods or by methods of solving partial differential equations. Both of these approaches are computationally time-consuming, especially when model parameters need to be estimated using samples from bond yield data. Therefore, the literature on determining the bond prices, starting with the works of Vasiček and Cox, Ingersoll and Ross, focused on solutions in a closed form. From a practical point of view it is interesting to consider the problem of how much the results obtained with the help of these models differ. The main purpose of this article is to obtain analytical solutions when analyzing the time structure of interest rates for the yield of zero-coupon bonds using the Cox-Ingersoll-Ross model in a single-factor and multifactor variants. It also compares the yield curves and forward curves resulting from the short-term interest rate behavior models mentioned above.

Keywords: yield interest rates, affine model, yield curve, forward curve, Vasiček model, Cox – Ingersoll – Ross model

JEL Classification: G12

Suggested Citation

Medvedev, Gennady, On Term Structure of Yield Rates. 2. The Cox – Ingersoll – Ross Model (January 20, 2012). Tomsk State University Journal of Control and Computer Science. 2012. No. 2(19). pp. 102-111., Available at SSRN: https://ssrn.com/abstract=2988959

Gennady Medvedev (Contact Author)

Belarusian State University ( email )

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